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a. We are given the firm’s MC curve: MC = 5 + 2q. This equation tells us that the firm’s MC curve has a
y-intercept of 5. Since the firm’s level of production when MC = 5 is 0 units we can extrapolate that when
the y-intercept of the market supply curve is 5, the market quantity produced is 0 units. Now, we need
another point on the market supply curve. So, return to your MC curve and pick a quantity (for example,
q = 1) and compute the MC for this quantity: thus, if q = 1, MC = 7. If one of the firms has MC of \$7
when it produces a quantity of one unit, this implies that if the market price is \$7 then there will be a total
of 10 units (since there are ten identical producers in this market). So, now you have two points on the
market supply curve: (Q, MC) = (0, \$5) and (10, \$7). Use these two points to find the linear market
supply curve:
P = 5 + (1/5)Q.
b. To find the short-run market equilibrium we need to find where the market demand curve intersects the
market supply curve. Thus, 5 + (1/5)Q = 17 – Q or Q = 10. Plug Q = 10 into either the market demand
curve or the market supply curve to find the equilibrium short-run market price: P = 17 – 10 = \$7 or P = 5
+ (1/5)(10) = \$7. To find the short-run level of production for the firm, set MR = MC or 7 = 5 + 2q or q =
1. With ten firms, each producing one unit of output that will provide us with the market output of 10
units.
c. Profits for a representative firm are equal to total revenue (TR) minus total cost (TC). TR = P*q = (\$7
per unit of output)(1 unit of output) = \$7. TC = 4 + 5(1) + (1)(1) = \$10. Short-run profits for a
representative firm are equal to -\$3.
To determine whether this firm will produce in the short-run or not we need to see if the TR is at least
large enough to cover the variable costs of production. From the TC curve we can see that fixed costs are
equal to \$4 (if q = 0, then TC = FC). So, variable costs (which vary as the level of output varies-a lesson I
hope you saw in problem 1 of this homework) can be written as VC = 5q + q*q and since q =1 that tells
us VC for the representative firm equal \$6. So, the TR of \$7 is greater than the VC of \$6, so this firm will
choose to produce in the short-run because its revenues are sufficient to cover its variable costs of
production.
Given that short-run economic profits for the representative firm are negative, we can anticipate that some
firms will exit the industry in the long-run. This will cause the market supply curve to shift to the left and
holding everything else constant result in a higher market equilibrium price, a smaller market equilibrium
quantity, and a larger level of production from those firms that remain in the industry.
d. To find the long-run equilibrium we start by recognizing that in the long-run the representative firm
will produce at that level of output where it earns 0 economic profit. This will occur where MR = MC =
ATC. We know the MC and we can find the equation for ATC. So, let’s start by equating these two
curves: MC = 5 + 2q and ATC = 4/q + 5 + q. Thus, 5 + 2q = 4/q + 5 + q or q = 4/q. We can rearrange this
to get q*q = 4 or q = 2 (in this example we don’t need to worry about the possibility that q = -2: a firm
cannot produce a negative level of output). When the firm produces 2 units of output, we get MC = 5 +
2(2) = \$9. Remember that MC = MR = ATC for the firm in long-run equilibrium: this implies that if MC
= \$9, then MR = \$9. If MR = \$9, this implies that the market equilibrium price is also \$9. Use this price
and the market demand curve to find the market quantity: P = 17 – Q or Q’ = 8 gadgets. With each firm
producing 2 gadgets and a total production of 8 gadgets, this implies that there are 4 firms in the industry
at the long-run equilibrium. So, six firms exited the industry in the long-run, P’ = \$9, Q’ = 8 gadgets, and
q’ = 2 gadgets. For the representative firm in the long-run, TR = (\$9 per gadget)(2 gadgets) = \$18 and TC
= 4 + 5(2) + (2)(2) = \$18: therefore, long-run profits for the firm are equal to zero.
3. Suppose that there is a monopoly that is described by the following information:
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