经济商业数学代写 ECONOMICS代写

MATHEMATICS FOR ECONOMICS AND BUSINESS

Midterm 2 Exam

经济商业数学代写 (i) find the value of Q which minimizes average cost (AC). [2 points] (ii) Show that at the AC minimizing of Q, the slope of MC > 0. [3 points]

(i) find the value of Q which minimizes average cost (AC). [2 points]

(ii) Show that at the AC minimizing of Q, the slope of MC > 0. [3 points]

(c) (i) What type of economic problem is solved by equating marginal product of labour and average product of labour? [Multiple choice] [1 point]

A. Maximise output

B. Maximise labour productivity

C. Maximise profit

D. Minimise marginal product of labour

E. Minimise average product of labour

(ii) At the profit maximizing quantity Q, the slope of marginal cost (MC) would be [Multiple choice] [1 point]

A. Equal to the slope of marginal revenue (MR)

B. Greater than the slope of marginal revenue (MR)

C. Less than the slope of marginal revenue (MR)

(b) Given

Q₁=50-4P₁-3P₂+2P₃+0.001Y

at P₁=5，P₂=7，P₃=3，Y=11000，Q₁=26

where Q₁ is quantityof good 1, P₁ , P₂ , P₃ are prices of goods 1,2,3, respectively. Y is income.

i) Use cross price elasticities to determine the relationship between good 1 and the other two goods. Comment on it. [2 points]

(ii) Determine the effect on of a 10 percent price increase for each of the other goods individually. Comment on it. [2 points]

iii) A decrease in P3 will shift the demand curve [Consider price on the vertical axis and quantity on the horizontal axis] [Multiple choice] [1 point]

A. leftward (downward)

B. Upward (rightward)

C. None of the above

iv) If the coefficient on reduces from -4 to -8, what will happen to the demand curve? [Consider price on the vertical axis and quantity on the horizontal axis] [Multiple choice] [1 point]

A. Move leftward (downward)

B. Move Upward (rightward)

C. None of the above

Question 3 (14 points) 经济商业数学代写

(a) A firm’s production function is given by

Q = K²+L²

where Q, L and K denote the number of units of output, labour and capital, respectively. Labour costs are $2 per unit, capital costs are $1 per unit. If the firm is prepared to spend $10 on input costs, then

(i) Find the stationary values of K and L. Show optimum points of K and L by drawing Isoquant and Isocost curves. [3 points]

(ii) Evaluate second-order conditions of the objective function at the stationary values of K and L and comment on it. [2 points]

(i) Find the profifit-maximizing level of price and outputs for each product. [4 points]

(ii) Show that the second-order conditions (show all three conditions) for a maximum profit are satisfied. [3 points]

iii) What would be the effect on firm’s profit if slope of demand function of Q₂increases? [Consider price on the vertical axis and quantity on the horizontal axis] [Multiple choice] [1 point]

A. No change in profit

B. Profit increases

C. Profit reduces

iv) What would be the effect on firm’s profit if intercept of demand function of Q₁increases? [Consider price on the vertical axis and quantity on the horizontal axis] [Multiple choice] [1 point]

A. No change in profit

B. Profit increases

C. Profit reduces

Question 4 (13 points) 经济商业数学代写

Given the four-sector macroeconomic model

(i) a $30 increase in autonomous import, M*

(ii) a 10 percent decrease in the marginal propensity to Import, m.

(b) ) If in part (a), we assume that the full employment level of income Y_fe=2075 and the government wishes to achieve it. Then, calculate the effect on the balance of payments (BOP) [BOP=X–M] [Show mathematically and explain in words] [5 points]

(i) if government achieve Y_fe=2075 through a $30 increase in government spending, G*.

(ii) if government achieve Y_fe=2075 through a $40 reduction in autonomous taxes, T*.

A. No change in T

B. T increases

C. T reduces

ii) What would be the effect on budget deficit (T-G) due to a decrease in G*? [Multiple choice] [1 point]

A. No change in budget deficit

B. budget deficit increases

C. budget deficit reduces

D. budget deficit will be 0 (zero)

Question 5 (15 points) 经济商业数学代写

A consumer’s utility function is given by

U=x^1/2+y^1/2

where x and y denote the number of items of two goods G1 an G2 that are bought. P_x and P_y are the prices of good x and y, respectively. M is consumer income. U denotes utility.

[Solve this question using Lagrange multiplier and Lagrangian function]

a) Write down budget constraint and Lagrangian function. [1 point]

b) Solve for optimum level of x and They are also called demand functions of good x and y, respectively. [5 points]

c) Show mathematically that both demand for good x and y are downward sloping. [4 points]

d) Show mathematically that the law diminishing marginal utility holds for both goods. [2 point]

e) Find the maximum value of U if budget constraint is 5x+5y=200. [1 point]

f) i) What would be the effect on utility, U if income increases to $300 from $200 and price of y increases to $10 from $5, assuming everything else is unchanged? [Multiple choice] [1 point]

A. No change in U

B. U increases

C. U reduces

D. None of the above

ii) Does a change in price of good y (P_y) change the value of the Lagrange multiplier, λ , assuming everything else is unchanged? [Multiple choice] [1 point]

A. Yes

B. No

Question 6 (15 points)

(i) Find or calculate the consumers’ surplus (CS). Calculate the change in consumer’s surplus (CS) due to an 8.8 percent increase in price. [5 points]

(ii) Sketch a graph of the demand function and shade the area, which corresponds to the change in consumer’s surplus calculated in part (i). [2 point]

iii) What would be the effect on consumer’s surplus (CS) due to an increase in the intercept of MC function from 4 to 7, assuming everything else is unchanged? [Use nearest (closest) integer quantity, Q] [Multiple choice] [1 point]

A. No change in CS

B. CS increase

C. CS reduces

D. CS will be 0 (zero)

iv) What would be the effect on consumer’s surplus (CS) due to an increase in the slope of MC function from 3 to 12, assuming everything else is unchanged? [Use nearest (closest) integer quantity, Q] [Multiple choice] [1 point]