# Managerial Economics

Assessment Questions

Your student number: Y 3 X X X __ __ __

a b c

Example: if your student number is Y3912345, then a=3, b=4, and c=5.

Question 1 (Lecture 3) 参考练习题第五题

Suppose that the demand curve for a product is given by

Qxd=100-2 Px+a Py,  ED = Q/P=横纵标的差值/纵坐标的差值=((Q2-Q1)/Q1)/((P2-P1)/P1)or(((Q2-Q1)/((Q2+Q1)/2))/（((P2-P1)/((P2+P1)/2）)）计算百分比。负号省略。

where Px = £20, where Py = £20 is the price of another product, and where a follows from your student number.

1. Give the values of a, b, and c that follow from your student number.

a = 6

b = 9

c = 3

(0 marks)

1. Calculate the demand for good X in this market at the current price level. How much revenue would the firm make?

Qxd=100-2 Px+a Py, where Px = £20, where Py = £20

100 – 2*20+6*20=180

-2*（20/180）= -2*（1/9）= -（2/9）

(2 marks)

1. If the firm wishes to increase total revenue, would it need to increase or decrease the current price of good X?

decrease

(4 marks)

1. Calculate the cross-price point elasticity 需求弹性between goods X and Y at the current price level. Are the goods complements or substitutes?

substitutes 6*（20/180）= 6/9

(4 marks)

• 必需品（inelasticity）, 奢侈品（elasticity）。
• 相近替代品的课获得性（substitutes）

Inelasticity

Elasticity

Question 2 (Lecture 4)

Brit-Brick is a company that produces bricks and cement in the UK. Their largest consumer is ConstrUK, a UK construction company. The manager of Brit-Brick has asked the research department to find out how sensitive ConstrUK’s demand for bricks is. The research department has estimated that ConstrUK’s preferences over bricks (x) and cement (y) can be described by the utility function

U(x,y) = xb/10 y1-b/10 ,

where b follows from your student number, and where x and y are measured in bags.

Example: if b=4, then U(x,y) = x4/10 y1-4/10= x2/5 y3/5.

The price for one bag of cement is equal to £1. It is estimated that ConstrUK’s budget is £10,000. Find the price-consumption curve for bricks and the corresponding demand curve.

B=9,

B = 9 , U (x,y) = x^(9/10)y^(1-9/10)=x^(9/10)y^(1/10)

(10 marks)

Question 3 (Lecture 5)

Consider a short run production function q=cL+K where the value for c follows from your student number, using L units of labour and K units of capital.

1. Compute the marginal product of labour.

Q= 3L+k

(7 marks)

1. Does the production function exhibit decreasing, increasing or constant returns to scale? Explain your answer. Decreasing

(3 marks)

Question 4 (Lecture 6)

(10 marks)

Question 5 (Lecture 7) According to Lecture 7

Suppose two firms face market demand of P=150-Q,

where Q=q1+q2

Both firms have the same unit cost of C, which consist of your student number a plus 20 (i.e. if your student number a=3, then cost C=20+3=23). Assume the firms compete a la Stackelberg. Firm 1 is the leader and Firm 2 is the follower in this market.

1. What is the follower’s total revenue function?

TR=（150-q1+q2-46）*(q1+q2) (3 marks)

1. Determine the equilibrium output level for both the leader and the follower. (3 marks)
2. Determine the equilibrium market price. (3 marks)
• Determine the profits of the leader and the follower. (1 marks)

Total Marks – 50 Marks

END OF ASSESSMENT QUESTIONS