Question #58969

Five hundred identical almond growers in region A have (long-run) total cost T CA =
q
2
100
where q is the number of crates a grower produces. Three hundred growers in region B have
(long-run) total cost T CB =
q
2
50 .
(a) nd the individual supply function for each type of almond grower
(b) \add up" all individual supplies to nd the almond industry supply function
(c) if the market demand for almonds is q
D(p) = 105; 000
2; 500p what will be the equilibrium
price of almonds? The equilibrium quantity? How much does each type of grower
produce? How much prot/loss they make?

Expert's answer

500 almond growers in region A have (long-run) total cost TCA = q^2 + 100

300 growers in region B have (long-run) total cost TCB = q^2 + 50.

(a) The individual supply function for each type of almond grower will be the part of MC curve after the intersection with ATC curve, so:

pS(A) = MC(A) = TC(A)' = 2q

pS(B) = MC(B) = TC(B)' = 2q

(b) To fi nd the almond industry supply function, we should add up all individual supplies, so pS = pS(a) + pS(B) = 2q + 2q = 4q, qS = p/4

(c) If the market demand for almonds is qD(p) = 105 - 500p, then the equilibrium is in the point, in which qD = qS and pS = pD, so:

105 - 500p = 0.25p

p = $0.21 - equilibrium price of almonds.

The equilibrium quantity is q = 0.21/4 = 0.05.

300 growers in region B have (long-run) total cost TCB = q^2 + 50.

(a) The individual supply function for each type of almond grower will be the part of MC curve after the intersection with ATC curve, so:

pS(A) = MC(A) = TC(A)' = 2q

pS(B) = MC(B) = TC(B)' = 2q

(b) To fi nd the almond industry supply function, we should add up all individual supplies, so pS = pS(a) + pS(B) = 2q + 2q = 4q, qS = p/4

(c) If the market demand for almonds is qD(p) = 105 - 500p, then the equilibrium is in the point, in which qD = qS and pS = pD, so:

105 - 500p = 0.25p

p = $0.21 - equilibrium price of almonds.

The equilibrium quantity is q = 0.21/4 = 0.05.

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