Suppose that in a perfectly competitive market, one individual firm uses two inputs: Labor (L) and Capital (K) and it has the production function, y = √LK. The prices of the inputs are WL = $1 and WK = $4. Assume that the number of firms in the industry can vary and all firms are identical. a. Show that the production technology exhibits constant returns to scale. b. Find the cost function of an individual firm, C(y). c. Derive and graph the average cost and marginal cost curve of an individual firm. d. Derive and graph the long-run industry supply curve. e. If the market demand is given by D(p) = 10 − p. How many units of output are traded in the long-run equilibrium? f. ) The government imposes a per-unit tax of $1. Find the tax incidence of the buyer and the seller.
Suppose that in a
inputs: Labor (L) and Capital (K) and it has the production function, y = √LK. The prices
of the inputs are WL = $1 and WK = $4. Assume that the number of firms in the industry can vary and all firms are identical.
a. Show that the production technology exhibits constant returns to scale.
b. Find the cost function of an individual firm, C(y).
c. Derive and graph the average cost and marginal cost curve of an individual
firm.
d. Derive and graph the long-run industry supply curve.
e. If the market demand is given by D(p) = 10 − p. How many units of output
are traded in the long-run equilibrium?
f. ) The government imposes a per-unit tax of $1. Find the tax incidence of the
buyer and the seller.
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