代写ECON 390-Economic of Networks Test 1-Spring 2024调试数据库编程

ECON 390-Economic of Networks

Test 1-Spring 2024

NAME:

Due date: February 7th by 11:59pm.

QUESTION 1 (25 Points)

Consider a market where

D(p) = α − βp   (Demand Curve) (1)

S(p) = γ + δp   (Supply curve) (2)

where α, β, gamma, δ > 0 and α > γ.

1. Find the unique equilibrium price p ? for this market, where (5 points)

p*S = p*D = p*.           (3)

2. Find the equilibrium quantity q ? , where (5 points)

S(p*S ) = D(p*D) = q*.                 (4)

3. Say the government imposes a quantity tax t on the demand D, so that equation (4) is changed to p*D = p*S + t. Find the new equilibrium price and equilibrium quantity.         (15 points)

QUESTION 2 (25 Points)

Consider a consumer with utility u(x, y) = √xy. The consumer has w to spend, and the price of x is px and the price of y is py:

1. Graph the budget line. (5 points)

2. Find the point that maximizes the consumer’s utility given the budget. (10 points)

Hint: 

3. Now assume that py increases to p 0y . What happen to the demand of x and y?. (5 points).

4. Now assume that w increases to w 0 . What happen with the demand of x and y? (5 points)

QUESTION 3 (25 Points)

A firm use two inputs l and k for producing its output. The production function of the firm is q = f(x, y) = Alαl1−α. The market price for l is w while the market price for r is r.

1. Find the combination of the l and k that minimizes the firm’s cost subject to a production level ¯q = f(k, l) = Alαl 1−α.

Hint: (10 points)

2. Now suppose that w increases to w 0 . What happen with the demand of k and l? (5 points)

3. Now suppose that ¯q increases to ˆq. What is the new production cost ? (10 points)

QUESTION 4 (25 Points)

In class, we discussed the first and second welfare theorems in the theory of general equi-librium

1. Discuss the similarities and differences of these two theorems. (10 points)

2. Explain why the existence of an equilibrium price is relevant. In particular, explain the relevance of this existence theorem to understand economic systems in the general equilibrium theory. (15 points)