problem 1: If demand is represented by Q_{d} = 50 -.5P +.005I where I is income and I = $50,000 and supply is represented by Q_{s} = 100 +.4P - 2W where W is wages and W = $15.00.
a) Compute the equilibrium price and quantity where wages = W = $15.00.
b) Compute the equilibrium price and quantity if income falls to I = $40,000?
c) Plot the demand and supply for the two income level. In the graph, mark all values that fully identify the curve.
problem 2: Suppose an investment can yield three possible cash flows with their probabilities given in the parentheses:
$600(p = 0.5); $-100 (p = 0.2) and $800 (p = 0.3).
a) Compute the expected value and the standard deviation of this investment. Is this investment risky? Why?
b) The equation E(x) = 359 + 0.5SD describes the indifference curve of this investor. Is this investor risk averse, risk neutral, or risk loving? describe your answer and draw the curve.
c) How much would this person pay for the investment opportunity (certainty equivalent of the current investment)? How much is risk premium for the current investment?
problem 3: Patrick consumes only two goods: Celtic Music concerts and Celtic Springs Water. Patrick earns $100 per month at his part-time job in the library. The price of Celtic concerts is $10. The price of Celtic Springs Water is $2. Patrick currently goes to 5 Celtic concerts and consumes 25 bottles of Celtic Spring Water in a month.
a) Draw Patrick's budget constraint and optimal consumption bundle. Please put Celtic concerts on the x-axis.
b) In April Patrick receives a 5% pay increase. Meanwhile the inflation raises the price of concerts to $10.50 and the price of Celtic Springs Water to $2.10. Draw Patrick's new budget constraint and optimal consumption bundle. Please put Celtic concerts on the x-axis. How many Celtic concerts does he attend in April? How many bottles of water does he drink in April?
problem 4: The demand equation for crossing the G.W.Bridge in New York City is P = 50-0.0001Q where P is the toll at the bridge and Q is the number of vehicles that cross the bridge every day.
a) Compute the toll that would maximize revenue for the state of New York. At this toll, how many cars would cross the bridge?
b) What is the price elasticity at this toll? describe your answer.
c) Also illustrate this price/quantity combination in a graph with demand curve and marginal revenue curve.
d) Suppose the company in charge of the maintenance of the bridge successfully negotiates a 20% increase in its annual fee. The State of New York hires you to advise them how to cover this cost. Would you advise them to raise the toll you computed in part a)? (Yes, or No, describe your answer). Would you advise them to raise revenue some other way? describe your answer.
problem 5: England and Scotland both produce scones and sweaters. Suppose that an English worker can produce 50 scones per hour or 1 sweater per hour. Suppose that a Scottish worker can produce 40 scones per hour or 2 sweaters per hour.
a) Which country has the absolute advantage in the production of each good? Which country has the comparative advantage?
b) If England and Scotland decide to trade, which commodity will Scotland trade to England? describe.
c) If a Scottish worker could produce only 1 sweater per hour, would Scotland still gain from trade? Would England still gain from trade?