Identify the firm’s supply curve on your graph.
The firm supply curve is the MC curve above the point where MC=AVC. The firm will produce at the point where price equals MC as long as MC is greater than or equal to AVC.
At what price would the firm supply exactly 6 units of output?
The firm maximizes profit by choosing the level of output such that P=MC. To find the price where the firm would supply 6 units of output, set q equal to 6 and solve for MC:
9. a. Suppose that a firm’s production
function is
in
the short run, where there are fixed costs of $1,000 and x is the
variable input, whose cost is $4,000 per unit. What is the total
cost of producing a level of output q. In other words, identify the
total cost function C(q).
The total cost function C(x) = fixed cost + variable cost = 1000 +
4000x. Since the variable input costs $4,000 per unit, the variable
cost is 4000 times the number of units, or 4000x. Now rewrite the
production function to express x in terms of q so that
.
We can then substitute this into the above cost function to find
C(q):
.
Write down the equation for the supply curve.
The firm supplies output where P=MC so the marginal cost curve is the
supply curve, or
.
If price is $1000, how many units will the firm produce? What is the level of profit? Illustrate on a cost curve graph.
To figure this out, set price equal to marginal cost to find:
.
Profit is 1000*10.125-(1000+(4000*10.125*10.125)/81) = 4062.5. Graphically, the firm produces where the price line hits the MC curve. Since profit is positive, this will occur at a quantity where price is greater than average cost. To find profit on the graph, take the difference of the revenue box (price times quantity) and the cost box (average cost times quantity). This rectangle is the profit area.
10. Suppose you are given the following information about a particular industry:
Assume that all firms are identical, and that the market is characterized by pure competition.
Find the equilibrium price, the equilibrium quantity, the output supplied by the firm, and the profit of the firm.
Equilibrium price and quantity are found by setting market supply
equal to market demand, so that 6500-100P=1200P. Solve to find P=5
and substitute into either equation to find Q=6000. To find the
output for the firm set price equal to marginal cost so that
and q=500. Profit of the firm is total revenue minus total cost or
Notice that since the total output in the market is 6000, and the
firm output is 500, there must be 6000/500=12 firms in the industry.
Would you expect to see entry into or exit from the industry in the long-run? Explain. What effect will entry or exit have on market equilibrium?
Entry because the firms in the industry are making positive profit. As firms enter, the supply curve for the industry will shift down and to the right and the equilibrium price will fall, all else the same. This will reduce each firm’s profit down to zero until there is no incentive for further entry.