Jonathan spends his income (M) on good X and Y. His preferences are represented by the utility function(X, Y) = Ln X + LnY. The price of good Y is 1 and the price of good X is PX. (a) Derive his demand for X and Y. (b) Jonathan’s father considers X and Y as merit goods and wants to encourage his son to consume more of them by offering him a subsidy of $1 for every unit of X that he purchases. Suppose the initial price of X is $2, derive the substitution effect of Jonathan’s demand for X with the subsidy when his income is $20. (c) Does the subsidy increase Jonathan’s consumption of Y?
9) Jonathan spends his income (M) on good X and Y. His preferences are represented by the
utility function(X, Y) = Ln X + LnY.
The
(a) Derive his demand for X and Y.
(b) Jonathan’s father considers X and Y as merit goods and wants to encourage his son to
consume more of them by offering him a subsidy of $1 for every unit of X that he
purchases. Suppose the initial price of X is $2, derive the substitution effect of
Jonathan’s demand for X with the subsidy when his income is $20.
(c) Does the subsidy increase Jonathan’s consumption of Y?
(d) How does the subsidy affect Jonathan’s total spending on X and Y.
(e) Instead of offering the subsidy, the father decides to spend the same amount of money
on Jonathan by offering him an income supplement. Is this a better alternative than
the unit subsidy in achieving the father’s objective?
12(a) Consider a
The cost function of a price-taking firm is given by C(q) = q3 − 2q^2 + 3q.
The market demand is Q = 30 − 4P.
Suppose factor costs are constant for the industry and there is free entry and exit.
(i) Derive the short-run supply function of a firm.
(ii) Derive the long-run
(iii) Determine the number of firms in the industry in the long-run equilibrium.
(iv) Discuss the incidence of the tax on consumers and producers in the long run if
the government imposes a unit tax of $t on every firm.
12(b)
(i) “Regulating a natural
level of output is counterproductive because it requires a subsidy that is
ultimately borne by taxpayers”. Evaluate the validity of this statement.
(ii) A monopolist has two types of customers with the following demand functions:
Demand of customer 1: Q1 = 80 − P1
Demand of customer 2: Q2 = 100 − P2
The monopolist has a constant marginal cost of 20 and no fixed costs.
Suppose the monopolist engages in third-degree price discrimination.
Find the equilibrium quantity and price charge to each type of customer?
Question 13
(a) Assume a closed economy with flexible prices and wages. Using the AD-AS
model, identify the impact of the following shocks in the short and in the long
run. Explain the adjustment process between the short and the long-run
equilibrium.
(i) Due to increased uncertainty about returns on investment, firms scale back or
defer their expansion plans.
(ii) Due to border closures, there is an increase in the logistical costs incurred by
firms in the production process.
(b) With reference to each of the two shocks described in (a) above, identify and
comment on possible policy responses if the government or the central bank wants
to avoid short run fluctuations in output and the price level.
(c) Use the
the government embarks on a program of fiscal expansion. Then explain how your
answer would change if agents in the economy believe that the central bank is fully
committed to maintaining stable inflation rates.
Question 14
(a) Explain, using the IS-LM-BP model, the impact of the following shocks to an open
economy. Border closures have led to a fall in tourism exports. You should assume
perfect capital mobility and consider the impact for both fixed and flexible exchange
rates.
(b) Now, using the same model, explain the impact on the economy, if the Central Bank
implements a policy of purchasing bonds on the open market. As in (a) above,
assume perfect capital mobility and consider the cases of both fixed and flexible
exchange rates.
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