1. (a) Suppose you are selling a product for $10 per unit in a competitive indus

Question

1. (a) Suppose you are selling a product for $10 per unit in a competitive industry; using the perfectly competitive model, showand explain what your profit will be if you sell 20 units at a cost of S5 per unit. b) What will you do to maximize profit if your marginal cost falls from $10 to $6? 2. Suppose you decide to manage a monopoly instead. If your demand and cost functions are estimated as follows: P-200-2Q and C (Q) (a) What is the price-quantity combination that will maximize profit? 1,200-2Q2 (b) What will be your maximum profit? (c.) What will be the maximum revenue to be obtained? Hint solve for MHR quantity, use the quantity to solve for price, and multiply price by MR quantity

Explanation / Answer

1.

a.) Perfect Competition is the situation prevailing in a market in which buyers and sellers are so numerous and well informed that all elements of monopoly are absent and the market price of a commodity is beyond the control of individual buyers and sellers; and this is why they earn Normal Profit.

Normal profit is a component of (implicit) costs and not a component of business profit at all. It represents the opportunity cost, as the time that the owner spends running the firm could be spent on running a different firm. The enterprise component of normal profit is thus the profit that a business owner considers necessary to make running the business worth his or herwhile i.e. it is comparable to the next best amount the entrepreneur could earn doing another job.

In the above case ; total revenue is $200
total cost is $100
profit = total revenue - total cost
= $100

b.) In perfect competition if marginal cost falls, to maximize profit supply is to be increased. like in the above case when price was $10 there was supply of 20 units know if Marginal cost is decreased to $6 the supply will be 28 units.

2. a) price-quantity combination to maximize profit
P = 200 - 2Q
  C(Q) = 1200 + 2Q2  
For Maximum profits, set MR = MC:
TR =P*Q
= (200-2Q)* Q
=200Q - 2Q2
MR = dTR/dQ
= 200 - 4Q
C(Q) = 1200 + 2Q2 =TC
MC = dTC/dQ = 4Q
therfore ; MR = MC
or, 200 - 4Q = 4Q
or, 8Q= 200
or, Q = 200/8
or, Q = 25
b)  Profit = TR-TC
TR = 200Q - 2Q2
= 200*25 - 2 * 252
= 5000 - 1250
= 3750

TC = 1200 + 2Q2
= 1200 + 1250
= 2450
PROFIT = 3750 - 2450
= 1300

C) MR = 200 - 4Q

= 200 - 100
= 100
therefore, maximum MR = 100 * 25 = 2500

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