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Demand and cost function
1. Indicate whether each of the following statements is true or false and
explain why.
a. A competitive firm that is incurring a loss should immediately cease
operations.
False. The condition for shut down in short run is that the price should be more than
average variable cost. A firm can be making losses under two circumstances.
1. If AVC>AR. In this case the firm is not able to able to recover its fixed costs in
short run and should immediately cease operations.
2. If AVC<AR but AC>AR...the firm is able to recover some of its fixed costs but still
be making losses. Since firm can cut its losses by continuing the operations in
short run it should continue its operations.
b. A pure monopoly does not have to worry about suffering loses because
it has the power to set its prices at any level it desires.
False. Although the firm is free to charge any price, the demand is determined by the
price charged by the monopoly. If it increases the price, the demand will decrease.
Generally, the marginal costs for a monopoly first decrease and then increase with
volume whereas the marginal revenues always decrease with increase in volume. If
there is no point on the graph where average cost is lower than the average revenues,
the monopoly will incur losses no matter however the price it can increase. Thus, it is not
always possible for the monopoly to make profits even by increasing price. Take one
such scenario in following graph. The monopoly will always make losses.
P
Q
Demand
AC
MC
MR
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c. In the long run, firms operating in perfect competition and monopolistic
competition will tend to earn normal profits.
True. A monopolistically competitive market has a small number of firms, which are
able to earn economic profits due to product differentiation achieved by these firms. As
new firms enter into the market, the competition will increase among these firms and
ability to distinguish the products from the competitors will become more and more
difficult leading to decrease in economic profits. Thus unless the firm is innovate and
introduce new products it will be able to earn only normal profits in long run. We can
give the similar logic for perfect competition.
d. Assuming a linear demand curve, a firm that wants to maximize its
revenue will charge a lower price than a firm that wants to maximize its
profits.
True. A profit maximization firm should produce at a level where MC=MR, whereas
the revenue maximizing firm should produce at a level where MR=0. Since demand
curve is linear, as we increase the volume, the MR will always fall (ever decreasing
function). Thus, the equilibrium price where we get MR=MC will always we greater
than the equilibrium price where we get MR=0 i.e. we are moving further down the
demand curve to achieve MR=0 and hence the price for revenue maximizing firm
will always be lower.
e. If P>AVC, a firm’s total fixed cost will be greater than its loss.
True. Since P>AVC, the firm will be able to recover some part of its fixed costs. Hence
its maximum losses will always be lower than its total fixed costs.
f. When a firm is able to set its price, its price will always be less than its
MR.
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False. A firm is able to set price in case of a monopoly. In case of monopoly, the
demand function is a decreasing function in P. Hence, P>MR
g. A monopoly will always earn economic profit because it is able to set
any price that it wants to.
False. The reason is same as explained in part b..
3. The demand and cost function for a company is estimated to be as
follows:
P = 100 8Q
TC = 50 + 80Q 100Q2 + 0.6Q3
Please check whether the question is correct. TC will become negative at q=2
and onwards, which is impossible. I feel the equation should be
TC=50+80Q-10Q^2+0.6Q^3
a. What price should the company charge if it wants to maximize
its profits in the short run?
For profit maximization set price where MR=MC
TR=P*Q=(100-8Q)*Q
Take differential w.r.t. Q to calculate
MR=d(TR)/dQ = 100-16Q
TC=50+80Q-10Q^2+0.6Q^3
Take differential w.r.t. Q to calculate
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MC=80-20Q+1.8Q^2
Equate MC=MR we get
80-20Q+1.8Q^2=100-16Q
1.8Q^2-4Q-20=0
Solve for Q we get 4.62
P=100-8*4.62=63
b. What price should it charge if it wants to maximize its revenue in
the short run?
For revenue maximization set MR=0
100-16Q=0
Q=6.25
P=100-8*6.25=50
c. Suppose the company lacks confidence in the accuracy of cost
estimated expressed in a cubic equation and simply wants to use
linear approximation. Suggest linear representation of this cubic
equation. What difference would it make on the recommended
profit-maximizing and revenue-maximizing prices?
Since P=100-8Q, the maximum range for Q is 12.5 (beyond this the price will become
negative which is infeasible. For the linear approximation we take the fixed cost as
same while the variable cost is worked out linearly. The variable cost at 12.5 units using
cubic function is TC=80*12.5-10*12.5^2+0.6*12.5^3=609.375
The slope for linear function is 609.375/12.5=52.75
The linear equation will be TC=50+52.75*Q
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For profit maximization MC=dTC/dQ=52.75
Setting MC=MR, we get 100-16Q=52.75
Q=2.95 and P=100-2.95*8=76.37
The quantity will decrease but price will increase.
For revenue maximization, the set price at MC=0
100-16Q=0
Q=6.25
P=100-8*6.25=50
Thus, only profit maximization price will change but revenue maximization
price will not change.
3. In the short run, firms that seek to maximize their market share
will tend to charge a lower price for their products than firms that
seek to maximize their profit. Do you agree with this
statement? Explain.
True. Reason similar to part d above.
In short run, a profit maximization firm should produce at a level where MC=MR,
whereas the revenue maximizing firm should produce at a level where MR=0. Since
demand curve is downward slopping, as we increase the volume, the price will
always fall and hence MR will always fall (ever decreasing function). Thus, the
equilibrium price where we get MR=MC will always we greater than the equilibrium
price where we get MR=0 i.e. we are moving further down the demand curve to
achieve MR=0 and hence the price for revenue maximizing firm will always be
lower.
However in long run both firms will produce at P=ATC
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### Unformatted Attachment Preview

Demand and cost function 1. Indicate whether each of the following statements is true or false and explain why. a. A competitive firm that is incurring a loss should immediately cease operations. False. The condition for shut down in short run is that the price should be more than average variable cost. A firm can be making losses under two circumstances. 1. If AVC>AR. In this case the firm is not able to able to recover its fixed costs in short run and should immediately cease operations. 2. If AVCAR...the firm is able to recover some of its fixed costs but still be making losses. Since firm can cut its losses by continuing the operations in short run it should continue its operations. Thus, answer is false. b. A pure monopoly does not have to worry about suffering loses because it has the power to set its prices at any level it desires. False. Although the firm is free to charge any price, the demand is determined by the price charged by the monopoly. If it increases the price, the demand will decrease. Generally, the marginal costs for a monopoly first decrease and then increase with volume whereas the marginal revenues always decrease with increase in volume. If there is no point on the graph where average cost is lower than the average revenues, the monopoly will incur losses no matter however the price it can increase. Thus, it is not always possible for the monopoly to make profits even by increasing price. Take one such scenario in following graph. The monopoly will always make losses. P Demand AC MC MR Q c. In the long run, firms operating in perfect competition and monopolistic competition will tend to earn normal profits. True. A monopolistically competitive market has a small number of firms, which are able to earn economic profits due to product differentiation achieved by these firms. As new firms enter into the market, the competition will increase among these firms and ability to distinguish the products from the competitors will become more and more difficult leading to decrease in economic profits. Thus unless the firm is innovate and introduce new products it will be able to earn only normal profits in long run. We can give the similar logic for perfect competition. d. Assuming a linear demand curve, a firm that wants to maximize its revenue will charge a lower price than a firm that wants to maximize its profits. True. A profit maximization firm should produce at a level where MC=MR, whereas the revenue maximizing firm should produce at a level where MR=0. Since demand curve is linear, as we increase the volume, the MR will always fall (ever decreasing function). Thus, the equilibrium price where we get MR=MC will always we greater than the equilibrium price where we get MR=0 i.e. we are moving further down the demand curve to achieve MR=0 and hence the price for revenue maximizing firm will always be lower. e. If P>AVC, a firm’s total fixed cost will be greater than its loss. True. Since P>AVC, the firm will be able to recover some part of its fixed costs. Hence its maximum losses will always be lower than its total fixed costs. f. When a firm is able to set its price, its price will always be less than its MR. False. A firm is able to set price in case of a monopoly. In case of monopoly, the demand function is a decreasing function in P. Hence, P>MR g. A monopoly will always earn economic profit because it is able to set any price that it wants to. False. The reason is same as explained in part b.. 3. The demand and cost function for a company is estimated to be as follows: P = 100 – 8Q TC = 50 + 80Q – 100Q2 + 0.6Q3 Please check whether the question is correct. TC will become negative at q=2 and onwards, which is impossible. I feel the equation should be TC=50+80Q-10Q^2+0.6Q^3 Please check else follow the same procedure but answers will be infeasible. a. What price should the company charge if it wants to maximize its profits in the short run? For profit maximization set price where MR=MC TR=P*Q=(100-8Q)*Q Take differential w.r.t. Q to calculate MR=d(TR)/dQ = 100-16Q TC=50+80Q-10Q^2+0.6Q^3 Take differential w.r.t. Q to calculate MC=80-20Q+1.8Q^2 Equate MC=MR we get 80-20Q+1.8Q^2=100-16Q 1.8Q^2-4Q-20=0 Solve for Q we get 4.62 P=100-8*4.62=63 b. What price should it charge if it wants to maximize its revenue in the short run? For revenue maximization set MR=0 100-16Q=0 Q=6.25 P=100-8*6.25=50 c. Suppose the company lacks confidence in the accuracy of cost estimated expressed in a cubic equation and simply wants to use linear approximation. Suggest linear representation of this cubic equation. What difference would it make on the recommended profit-maximizing and revenue-maximizing prices? Since P=100-8Q, the maximum range for Q is 12.5 (beyond this the price will become negative which is infeasible. For the linear approximation we take the fixed cost as same while the variable cost is worked out linearly. The variable cost at 12.5 units using cubic function is TC=80*12.5-10*12.5^2+0.6*12.5^3=609.375 The slope for linear function is 609.375/12.5=52.75 The linear equation will be TC=50+52.75*Q For profit maximization MC=dTC/dQ=52.75 Setting MC=MR, we get 100-16Q=52.75 Q=2.95 and P=100-2.95*8=76.37 The quantity will decrease but price will increase. For revenue maximization, the set price at MC=0 100-16Q=0 Q=6.25 P=100-8*6.25=50 Thus, only profit maximization price will change but revenue maximization price will not change. 3. In the short run, firms that seek to maximize their market share will tend to charge a lower price for their products than firms that seek to maximize their profit. Do you agree with this statement? Explain. True. Reason similar to part d above. In short run, a profit maximization firm should produce at a level where MC=MR, whereas the revenue maximizing firm should produce at a level where MR=0. Since demand curve is downward slopping, as we increase the volume, the price will always fall and hence MR will always fall (ever decreasing function). Thus, the equilibrium price where we get MR=MC will always we greater than the equilibrium price where we get MR=0 i.e. we are moving further down the demand curve to achieve MR=0 and hence the price for revenue maximizing firm will always be lower. However in long run both firms will produce at P=ATC Name: Description: ...
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