1. The market for tortillas is perfectly competitive, with market demand for pac
ID: 1248293 • Letter: 1
Question
1. The market for tortillas is perfectly competitive, with market demand for packages of tortillas given by P=1 .-00002Q, with price in dollars per package and Q in thousands of packages. The short-run marginal cost curve for a typical tortilla factory is MC = .05 .00+05q, with MC in dollars per package and qin thousands of packages. The fixed cost of running a tortilla factory is $10,000 per firm.
(a) If there are 100 identical factories, determine the short-run industry supply function.
(b) What is the market equilibrium quantity of tortillas, and what is the equilibrium price?
(c) At this output level, what is the typical factory's producer's surplus?
(d)What is the typical factory's profit?
Explanation / Answer
a).
The long-run supply comes from adding together the quantities supplied by all factories at a given
price. The graphical illustration is in the graph below. Algebraically, to sum the quantities, you must
solve for q as a function of MC. Doing this for a typical tortilla factory, one gets
q1 = (MC - .05)/.0005.
Adding two of these together, for factories 1 and 2, one gets
q1 = (MC - .05)/.0005
q2 = (MC - .05)/.0005
Q = q1 - q2 = 2(MC - .05)/.0005
Note that q" and q# have subscripts, to keep track of which factory's quantity we're adding to the total,
but MC does not have a subscript. This is because, by definition, the aggregate supply is the sum of
quantities supplied by individual firms for a given price that is the same for all.
By extension, doing the sum for 100 identical factories gives Q oe 100(MC - .05)/.0005.
Solving back for MC as a function of Q, the aggregate supply curve is MC = .05 + .000005Q.
b.)
The market equilibrium quantity of tortillas comes from equating the aggregate supply with the market
demand curve: MC = .05 + .000005Qc = 1 - .00002Qc = P, where Qc denotes the market
equilibrium quantity. Solving, this is Qc = (1 - .05)/(.000005 + .00002) = .95/.000025 = 38,000, or
38 million packages (since q is defined in thousands of packages). The equilibrium price is
P = 1- .00002(38,000) = .24, or $0.24/package.
c.)
At this aggregate output level, with price of $0.24 per package, individual firms who set price equal to
marginal cost will produce qc according to
P = .24 = .05 + .0005qc = MC,
so the typical factory will produce qc = (.24 - .05)/.0005 = 380, or 380 thousand packages.
Producer's surplus will be PS=½($.24/package - $.05/package)(380,000 packages) = $36,100.
(d)
The typical factory's profit is $26,100, since profit is producer's surplus minus fixed costs.
Please,rate! Thank you.
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