problem1)
The price elasticity (ε) of demand for Q has been estimated at -0.5. Current consumption Q* is 70 units and market price (P*) is 0.70.
a) Fit the linear demand curve to a observed market data. Illustrate your result using a suitably labelled diagram. Hint: εB(P^{*}/Q^{*}) a and the equation for a linear demand function is Q^{*}= a - bP^{*}
b) Now assume that price of Q increases to P* = 0.80. Using your estimated demand function, find out the change in consumer surplus arising from the price increase. Illustrate your result.
problem 2)
Zac consumes only pizza and chianti. He consumes these goods in fixed proportions: 2 slices of the pizza for one glass of chianti. His income is $100 per week.
a) Derive demand functions for the pizza and chianti. Are the goods normal or inferior, substitutes or complements?
b) If pizza costs $1 per slice and chianti $3 per glass, how much of each good will he consume?
c)If price of pizza falls to $0.5 per slice and, chianti stays at $3 per glass, how much of each good will Zac consume?
d) Using suitably labelled diagram with pizza on a horizontal axis, illustrate the impact of a change in price of pizza from $1 to $0.5 per slice. Show the level of utility before and after the price change and show the decomposition line.
problem 3)
A consumer purchases food (X) and clothing (Y). Her utility function is given by:U(X,Y) = XY +10X , income is $100 and the price of food is $1 and the price of clothing is P_{y}.
a) Derive an equation for consumer’s demand function for clothing.
b) Are X and Y normal goods?
problem 4)
Firm’s production function is given by Q= 20√LK. The price of labour is w and the price of capital is r.
a) The price of labour is $5 and the price of capital is $20. What is the cost minimising combination of labour and capital if the firm wants to produce 1000 units per year?
b) Derive total cost function, as the function of Q, w and r.Substitute the values w = $5 and r = $20 into the cost function and illustrate LRTC(Q), LRAC(Q) and LRMC(Q) using a suitably labelled diagram (LR = long run). Why is the LRTC function shaped the way it is?
c) Now assume that capital is fixed at K‾ , derive the short run total cost function, using w = $5 and r = $20.Illustrate the SRTC(Q), SRAC(Q) and the SRMC(Q) functions using a suitably labelled diagram (SR = short run).