英譯漢,請厲害的人士幫忙
This mower uses 1 gallon of gasoline per hour and cuts 3 units of lawn per hour.
a)\x05Verify that the production functions for the two mowers are as follows:
Assume that z1 is hours of labor,z2 is gallons of gasoline,and z3 and z4 are
the hours of the small mower and the large mower,respectively.
b) Derive the cost functions
c) Show that using the small mower is a cheaper way to cut grass if 2w1＜W4
一3w3.Why is this result independent of the price of gasoline?
d) How high a price must our college student receive for cutting a unit of lawn
in order to induce her to set up her own lawn-mowing firm rather than work
in the family business?
5.Assume that a firm uses two types of input in the production of a certain commodity.
What is the maximum output if the marginal product of input 1 is MPI＝100X2一X1
and the marginal product of input 2 is MP2＝100X1一凡,the total amount that can be
spent on inputs is $1,000,the price of input 1 is $2,and the price of input 2 is $5?
6.Suppose that a firm has long-run total costs of $1,000 for producing 100 units of out-
put.The two inputs for production are labor and capital.Labor costs $10 per unit,and
capital costs $10 per unit.The firm is currently producing 100 units of output and is
using the cost-minimizing combination of 50L and 50K for labor and capital.
a) On an isoquant diagram,show that an increase in output from 100 units to
150 units will result in higher short-run than long-run total costs,average
costs,and marginal costs.
b) Show that a decrease in output from 100 units to 50 units will result in higher
short-run than long-run total costs and average costs but higher long-run than
short-run marginal costs
c) Give an intuitive explanation for these relationships between the short-run
and long-run cost curves.
7.Suppose that a firm produces a product with two inputs:labor and capital.Labor costs
$3 per unit of input,and capital costs $5 per unit.The firm maximizes output subject
to the constraint that it does not spend more than $1,000.
a) Draw a graph depicting the firm's cost constraint.Give the firm a set of con-
vex isoquants,and show an optimum for the firm on the graph.Label the op-
timal quantities of capital and labor and the isoquant associated with the opti-
mum so that the firm is producing 100 units of output.
b) Using the same isoquants that you used in Part a,show an optimum for the
firm that minimizes costs subject to the constraint that y＝100.What is the
level of costs at the new optimum?How do the optimal quantities of capital
and labor here compare to those you found in Part