Question

Question 5 120 marks] The Hobbits of the Shire are trying to decide how much bread and how much wine to produce. With the help of the information in the table, answer the following questions. Wine Bread ombination kthousands of bottles per thousands of loaves per year) ear 0 20 18 4 12 Willingness to Wine thousands ofpay bottles per(loaves of bread ear er bottle of wine) 2.0 1.5 1.0 a) Draw the Shire's production possibilities frontier. Put wine on the horizontal axis. (5 marks) b) What is the opportunity cost of the first two thousand bottles of wine? What is the marginal cost of the 3,000th bottle of wine? What is the marginal cost of the 3,000th loaf of bread? (5 marks) c) Draw the marginal cost of wine curve. What happens to the marginal cost if production of wine increases? Why? d) Draw the marginal benefit from wine curve on the same figure on which you put the marginal cost curve. Describe the relationship between the quantity of wine produced and the marginal benefit from wine. marks) e) What combination of bread and wine will you recommend the Hobbits to produce? Why? Explain to the Hobbits why they would be worse off by producing a different combination of bread and wine. (5 marks) (5 (5 marks)

Answer 1

Reservation wage is the wage at which a worker is indifferent between working or not working. This can be found by dividing the Non-labour income by total working hours.

Hence, we get reservation wage /hour

Reservation wage is the wage at which a worker is indifferent between working or not working. This can be found by dividing the Non-labour income by total working hours. Hence, we get reservation wage W_e = 215/110 = dollar 1.954/hour Since the wage that he will get $13.5 is more than his reservation wage, he will choose to work. (b) b. The bundle (C*, l*) that gives Elfi the maximum happiness should be the one maximising his utility function subject to both the budget and time constraints . (c) . The constraints can be given as B C: C = (T - l) w + Y where, C = Consumption level: T = total working hours available: l = leisure hours: w = hourly wage rate: Y = non-labour income and TIME CONSTRAINT TC T = h + l where h = hours worked d. Inserting the values that we know in the two constraints gives us, C =

Since the wage that he will get $13.5 is more than his reservation wage, he will choose to work.

b. The bundle (C*,l*) that gives Elfi the maximum happiness should be the one maximising his utility function subject to both the budget and time constraints.

c. The constraints can be given as

where, C= Consumption level; T=total working hours available; l=leisure hours; w=hourly wage rate; Y=non-labour income

and

TIME CONSTRAINT TC

where h= hours worked

d. Inserting the values that we know in the two constraints gives us,

and

which we have substituted in the BC

We now need to solve Elfi's utility maximisation problem using a Lagrangean method,

Setting up the Lagrangean L

First order conditions give us

and

Equating these two together, gives us

We use this in the BC to get

e. We check the values of C*, l* in the BC

C+13.5l=1700

or

850.425+13.5*62.935=1700

(Hence it satisfies the BC)

f. Level of utility that Elfi derives from the bundle C*, l* is given by

g. If Elfi's wage goes up to $18.5 an hour there is an opposing income and substitution effect. An increase in wage causes the price of leisure to go up, hence it causes leisure hours to fall. However, an income effect is also in place. It suggests that the value of endowment time goes up, hence makes Elfi reduce labour supply. The overall effect depends on which of the income or substitution effect dominates?

h. Solving the labour-leisure time allocation for the new wage rate, we get'

FOCS

Solving these two simultaneously gives us

Using this in BC gives

i. Elfi's leisure hours reduced. Hence Substitution effect dominates.