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□ Emily has decided to spend one-third of her income on clothing. What is Emily’s demand curve for clothing?
□ Emily’s taste – as reported in the previous question - has now changed. She now realizes the importance of savings and spends only one-tenth of her income on clothing, instead of one-third. How will Emily’s demand curve change?
The production function of a firm is given as
f(x)=20x-x2
The price of output is equal to 1. Let w be the price of the x-input. We must have x > 0.
a) What is the first-order condition for profit maximization if x > 0?
b) For what values of w will the optimal x be zero?
c) For what values of w will the optimal x be 10?
d) What is the factor demand function?
e) What is the profit function?
f) What is the derivative of the profit function with respect to w?
The technology for a firm is given as
Y=xa where 0 < a < 1
a) Obtain the demand for x and supply of y for this firm.
b) Derive the profit function of this firm.
c) From determine its degree of homogeneity.
d) Obtain the Hessian using above and show that it is convex in p and w.
Determine the elasticity of substitution of the Constant Elasticity of Substitution (CES) production function given below by obtaining its degree of homogeneity.
If the inverse demand curve of profit maximizing monopolist is given as P =1200 − 2Q , and cost function as
C = Q3 − 61.25Q2+1528.5Q + 2000, find equilibrium output level, monopolist price, and profit.
If the inverse demand curve of profit maximizing monopolist is given as P =1200 − 2Q , and cost function as
C = Q3 − 61.25Q2+1528.5Q + 2000, find equilibrium output level, monopolist price, and profit.
The following is a straight-line demand curve that confronts a single firm.
Quantity
Price demanded (3) (4)
$6 1 _____ _____
5 2 _____ _____
4 3 _____ _____
3 4 _____ _____
2 5 _____ _____
1 6 _____ _____
(a) In column 3, compute total revenue. In column 4, compute the coefficient for the price elasticity of demand at each price using the midpoints formula.
were much worse off, but farmers whose crops
were not destroyed benefited from the floods.
Why?
b. What information would you need about the
market for wheat in order to assess whether
farmers as a group were hurt or helped by the
floods?
Labor Total Product
0 0
1 20
2 50
3 70
4 80
5 85
6 82
If pen sells for Rs 3 per unit and workers can be hired in a competitive labor market for Rs30
per day, how many workers should be hired? Explain your answers clearly.
#340153 on Dec 2023