3. Let the market be perfectly competitive. Firms in the market produce output y using three factors of production (inpu
Posted: Sun May 08, 2022 9:11 am
3. Let the market be perfectly competitive. Firms in the market
produce output y using three factors of production (inputs), labour
L, capital K, and the raw material valerium V. Each firm’s
production function is 𝑓(𝐿,𝐾, 𝑉) = 𝐿 1 3𝐾 1 3𝑉 1 3 The wage rate is
w, the rental price of capital is r, and the price of valerium is
z.
a. Find the long run equilibrium price p in this competitive
market: 𝑝 = 𝑝(𝑟, 𝑤, 𝑧). (12)
b. Suppose in the short run, capital is fixed at K = 8 and
valerium is fixed at V = 1. Find the firm’s short run supply curve
as a function of the output price p: 𝑦 = 𝑦(𝑝). (6)
3. Let the market be perfectly competitive. Firms in the market produce output y using three factors of production (inputs), labour L, capital K, and the raw material valerium V. Each firm's production function is 1 1 1 f(L,K,V) = L3K3V; = The wage rate is w, the rental price of capital is r, and the price of valerium is z. a. = Find the long run equilibrium price p in this competitive market:p pír,w,z). (12) b. Suppose in the short run, capital is fixed at K = 8 and valerium is fixed at V = 1. Find the firm's short run supply curve as a function of the output price p: y = y(p). (6)
produce output y using three factors of production (inputs), labour
L, capital K, and the raw material valerium V. Each firm’s
production function is 𝑓(𝐿,𝐾, 𝑉) = 𝐿 1 3𝐾 1 3𝑉 1 3 The wage rate is
w, the rental price of capital is r, and the price of valerium is
z.
a. Find the long run equilibrium price p in this competitive
market: 𝑝 = 𝑝(𝑟, 𝑤, 𝑧). (12)
b. Suppose in the short run, capital is fixed at K = 8 and
valerium is fixed at V = 1. Find the firm’s short run supply curve
as a function of the output price p: 𝑦 = 𝑦(𝑝). (6)
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