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ECON 281 - B05: Intermediate Microeconomic Theory I

Winter 2024

Assignment 2

Due: 2024-02-16 In Class (by 3:50PM)

Part A – Short Answer

Please use graphs, formulas, or concise sentences to answer the questions below. When using graphs, please clearly label the axes, lines (or curves) and necessary points.

Full marks will be awarded if your answers are justified. (20 marks, 5 marks each)

1. Suppose the demand function of a good is Q = 30 − 2P. If the price of that good increases from $5 to $10, what is the change in the consumer surplus? Graph the demand curve and highlight the change in consumer surplus.

2. Suppose Bob has to decide how to allocate his total income of $300 between how many hours (H) at the gym and how many units of composite goods (Y) to purchase. The local gym charges $5 per hour, but $2 per hour if he pays the membership fee of $100. Write down the equations of both budget lines, and plot them in the same graph.

3. Suppose the utility function of a consumer is U(X, Y) = √XY, the marginal utilities are MUX = 2/1X−2/1Y2/1 and MUY = 2/1X2/1Y−2/1. The price of Y is $2, and the total budget of the consumer is $50. What is the consumer’s demand function for X?

4. Suppose the demand function of consumer A is QA = 20 − 2P and the demand function of consumer B is QB = 15 − P. Write down the market demand function Qm, and plot QA, QB and Qm in the same graph.

Part B – Long Answer

Please show all the steps to your solution. When using graphs, please clearly label the axes, lines (or curves) and necessary points.

Full marks will be awarded if your answers are justified. (80 marks, 20 marks each)

If your answer is not an integer, you may round it to 2 decimal places.

1. Suppose there are two goods X and Y. Eddie’s utility function is given by U(X, Y) = 3X + 2Y. Marginal utilities are MUX = 3, MUY = 2. The price of X and Y are $2 and $1, respectively. His total budget is $40.

(1) Write down the equation for Eddie’s budget line. Graph the budget line with X on the horizontal axis. What is the slope of this budget line?

(2) Plot three indifference curves corresponding to the utility levels of 54, 72, 90 on the same graph in (1). What is the slope of Eddie’s indifference curves?

(3) What is the optimal basket that Eddie will purchase? How much utility does the basket provide?

2. Suppose there are two goods X and Y. Jane’s utility function is given by U(X,Y)=min(X,2Y). The price of X and Y are $2 and $4, respectively. Her total budget is $80.

(1) Write down the equation for Jane’s budget line. Graph the budget line with X on the horizontal axis. What is the slope of this budget line?

(2) Plot three representative indifference curves corresponding to the utility levels of 5, 15, 25 on the same graph in (1). Draw a new line that passes the origin and all the 3 kinked points of the indifference curves. What is the slope of this new line?

(3) What is the optimal basket that Jane will purchase? How much utility does the basket provide?

3. Suppose there are two goods X and Y. John’s utility function is given by U(X, Y) = XY. Marginal utilities are MUX = Y, MUY = X. The price of X and Y are $4 and $1, respectively. His total budget is $40.

(1) What is the optimal basket that John will purchase?

(2) Suppose price of X now decreases to $2, what is the optimal basket of John now?

(3) Decompose the substitution effect and income effect of the price decrease. Find the intermediate basket, and calculate the substitution effect and income effect on John’s purchase of X and Y.

(4) Calculate the compensating variation and the equivalent variation resulting from the price decrease.

4. Consider a labour-leisure choice model of Mary. Mary’s utility function of leisure L and the composite good Y is U(L, Y) = 3L3/1Y3/2, The marginal utilities are MUL = L−3/2Y3/2 and MUY = 2L3/1Y−3/1. The hourly wage rate of Mary is w.

(1) Write down the equation for Mary’s budget line.

(2) What is the optimal choice of L and Y that Mary will choose?

(3) Will an increase wage w will change Mary’s choice of L? What about Y? Use w = 10 and w = 20 to illustrate.