A cost-minimizing firm has the following short-run production function:
Q=f (L,K)=72L+5L2-0.2L3
a) Briefly explain why this is a short-run production function.
b) At what level of employment would be diminishing returns set in for the variable input?
c) Fin the levels of employment that define stage two in the production process.
d)If the market-determined real wage rate is $20 determine the amount of labor a cost-minimizing firm would hire in order to minimize the total cost of production.
2) a) Briefly explain the concept of "Return to scale". What form of "Return toScale" does the following production function exhibit? Explain
b) Q=f(L,K)=L0.3 K0.7
Suppose a cost-minimizing firm wishes to change its scale of production and needs to know the combination of labor and capital to employ. If the first's total cost outlay is $14. Fin this combination using the information below and given that the prices of labor and capita are $1 and $3 per unit respectively.
Q= 0 1 2 3 4 5 6 7 8
TPI=0 11 20 28 35 41 45 46 46.5
TPK=0 24 45 63 78 87 93 96 97
where TPI AND TPK represent the total product of labor and total product of capital respectively.
3) Given the demand and supply schedules for semiconductors in a perfectly competitive market:
Qd=60-10P+0.5I, Qs=-10+4P-2C
Where I=average income of the demanders of this production
C=unit cost of the inputs used in the production of this commodity.
a) Find the expression for equilibrium price and equilibrium quantity transcended in this market.
b)Find the initial equilibrium and equilibrium quantity ifI=1000 and C=20
c) Determine the impact of an increase in income from 1000 to1200 on the initial equilibrium values.
d) Assume that an improvement in the technology of producing this commodity results in an increase in supply by a factor of 5, how will this development affect the initial equilibrium values?0
A cost-minimizing firm has the following short-run production function:
Q=f (L,K)=72L+5L2-0.2L3
a) Briefly explain why this is a short-run production function.
b) At what level of employment would be diminishing returns set in for the variable input?
c) Fin the levels of employment that define stage two in the production process.
d)If the market-determined real wage rate is $20 determine the amount of labor a cost-minimizing firm would hire in order to minimize the total cost of production.
2) a) Briefly explain the concept of "Return to scale". What form of "Return toScale" does the following production function exhibit? Explain
b) Q=f(L,K)=L0.3 K0.7
Suppose a cost-minimizing firm wishes to change its scale of production and needs to know the combination of labor and capital to employ. If the first's total cost outlay is $14. Fin this combination using the information below and given that the prices of labor and capita are $1 and $3 per unit respectively.
Q= 0 1 2 3 4 5 6 7 8
TPI=0 11 20 28 35 41 45 46 46.5
TPK=0 24 45 63 78 87 93 96 97
where TPI AND TPK represent the total product of labor and total product of capital respectively.
3) Given the demand and supply schedules for semiconductors in a perfectly competitive market:
Qd=60-10P+0.5I, Qs=-10+4P-2C
Where I=average income of the demanders of this production
C=unit cost of the inputs used in the production of this commodity.
a) Find the expression for equilibrium price and equilibrium quantity transcended in this market.
b)Find the initial equilibrium and equilibrium quantity ifI=1000 and C=20
c) Determine the impact of an increase in income from 1000 to1200 on the initial equilibrium values.
d) Assume that an improvement in the technology of producing this commodity results in an increase in supply by a factor of 5, how will this development affect the initial equilibrium values?0
