Introduction to Economics
Tutorial Four - Answers
1. An allergy pill sells for £25 a box. Steve, Maria, and Brian are willing to pay £33, £27, and
£19, respectively, for a box of pills. What is the total consumer surplus?
Answer:
Note that Brian does not buy pills because his willingness to pay is below the market price. So, for
Steve and Maria, the total consumer surplus is: (33-25) + (27-25) = 10.
2. Suppose John derives utility from consumption C and leisure l. He has the following
Cobb-Douglas utility function: U = (24-H)0.5(C)0.5, where w is the wage rate, H are the daily
hours of work, and C is total consumption.
i) What is John’s budget constraint?
ii) Set up the utility maximization problem.
iii) Derive John’s labor supply function.
Answer:
John solves the problem Max U = (24-H)0.5(C)0.5 subject to C = wH
Plugging the budget constraint into the utility yields U = (24-H)0.5(wH)0.5
Computing the FOC with respect to H yields:
- 0.5(24-H)-0.5(wH)0.5 + (24-H)0.5 0.5w(wH)-0.5= 0
Rearranging yields:
24-H = wH/w
24 - H = H
H* = 12
3. Meg's Sticks Ltd. produces hockey sticks with a production function given by
𝑞 = 2√𝐾𝐿. Assume capital K is fixed at 100 and labour L is variable, the rental rate of
capital is £1 and the wage rate of labour is £4.
i) Sketch the short-run production function, derive and sketch the average and marginal
product of labour functions, and state whether the marginal product of labour is increasing,
decreasing or constant.
Answer: SR production function is q = 20 L0.5. Sketch should show q as an increasing,
concave, function of L, with q = 0 when L = 0.
APL = q/L = 20/L0.5. MPL = dq/dL = 10 L-0.5. Sketch should show both functions are positive,
decreasing with L. Because APL is decreasing, MPL is always below APL.
MPL is decreasing.
ii) Calculate the firm's short-run total cost (SRTC), average cost (SRAC) and marginal cost
(SRMC).
Answer:
q = 20 L0.5, so L = q2/400.
Tutorial Four - Answers
1. An allergy pill sells for £25 a box. Steve, Maria, and Brian are willing to pay £33, £27, and
£19, respectively, for a box of pills. What is the total consumer surplus?
Answer:
Note that Brian does not buy pills because his willingness to pay is below the market price. So, for
Steve and Maria, the total consumer surplus is: (33-25) + (27-25) = 10.
2. Suppose John derives utility from consumption C and leisure l. He has the following
Cobb-Douglas utility function: U = (24-H)0.5(C)0.5, where w is the wage rate, H are the daily
hours of work, and C is total consumption.
i) What is John’s budget constraint?
ii) Set up the utility maximization problem.
iii) Derive John’s labor supply function.
Answer:
John solves the problem Max U = (24-H)0.5(C)0.5 subject to C = wH
Plugging the budget constraint into the utility yields U = (24-H)0.5(wH)0.5
Computing the FOC with respect to H yields:
- 0.5(24-H)-0.5(wH)0.5 + (24-H)0.5 0.5w(wH)-0.5= 0
Rearranging yields:
24-H = wH/w
24 - H = H
H* = 12
3. Meg's Sticks Ltd. produces hockey sticks with a production function given by
𝑞 = 2√𝐾𝐿. Assume capital K is fixed at 100 and labour L is variable, the rental rate of
capital is £1 and the wage rate of labour is £4.
i) Sketch the short-run production function, derive and sketch the average and marginal
product of labour functions, and state whether the marginal product of labour is increasing,
decreasing or constant.
Answer: SR production function is q = 20 L0.5. Sketch should show q as an increasing,
concave, function of L, with q = 0 when L = 0.
APL = q/L = 20/L0.5. MPL = dq/dL = 10 L-0.5. Sketch should show both functions are positive,
decreasing with L. Because APL is decreasing, MPL is always below APL.
MPL is decreasing.
ii) Calculate the firm's short-run total cost (SRTC), average cost (SRAC) and marginal cost
(SRMC).
Answer:
q = 20 L0.5, so L = q2/400.
