5SSPP217: Microeconomics
PROBLEM SET 5 (for week 7 tutorials)
1. Firm A has the following technology: f(x1; x2) =√(x1x2). The price of input 1 is w1 = 8
and the price of input 2 is w2 = 2. The firm A wants to produce y units of output. Find
analytically the conditional factor demand for the two inputs. Draw an isoquant a
several isocost lines. Locate the cost-minimising input bundle. Explain the intuition
behind the optimality condition you have found. What is the cost function?
2. A cost-minimising firm has production function y = min{4x1,x2}. Input prices are w1
and w2.
a) For a given target output Y, draw the corresponding isoquant and a number of
isocost lines. Identify in the graph the cost minimising input bundle.
b) Find analytically the cost minimising bundle and the resulting cost function.
3. A cost-minimising firm has production function y = L + 2K. Input prices are wL for
labour and wK for capital.
a) For a given target output Y, draw the corresponding isoquant and several isocost
lines with different slopes. Identify in the graph the cost minimising input bundle
in each case.
b) Find analytically the cost minimising bundle and the resulting cost function as a
function of the ratio wL/ wK.
4.
A firm’s cost function is given by c(y) = 4000 + 5y + 10y2.
a) Write an expression for each of the following cost concepts and draw the resulting
curves:
i. Total Fixed Cost
ii. Average Fixed Cost
iii. Total Variable Cost
iv. Average Variable Cost
v. Average Total Cost
vi. Marginal Cost
b) Find analytically the quantity that minimizes average total cost. Demonstrate that
the marginal cost is higher (lower) than average cost for output levels above
(below) that quantity.
5.
Domination Pizzas’ short-run cost function is C(y, K) = 17y2/32K + 0.25K, where y
is the number of pizzas produced and K is the number of ovens it uses. Currently,
Domination Pizzas is leasing 4 ovens in the short run.
a) Calculate the average cost of producing 10 pizzas.
b) The manager of Domination is considering leasing 10 additional ovens. What
would be then the average total cost of producing 10 pizzas? Would it be higher
or lower than the average cost with 4 ovens? Why?
c) Find Domination’s long run cost function. From it, establish whether
Domination’s technology exhibits increasing, constant, or decreasing returns to
scale.