Economics 201

1. The demand equation for commodity X is P = 160 - 3X, and the supply equation for the same good is P = 5X. Calculate:

a. The equilibrium price and quantity

b. The supply and demand elasticities at the equilibrium point [Hint: you do not need calculus here; use the geometrical formula in the Course Notes, p. 12]

c. The surplus that would result if a minimum price were imposed at P = 130.

2. A commodity's supply and demand have the following equations: S: X_{s} = -6 + 2P and D: X_{d} = 36 - 4P. The government subsidizes producers of this commodity at the rate of $3/unit. Calculate the cost of the subsidy. [ Hint: a subsidy is the opposite of a tax, so it LOWERS the supply curve instead of raising it. One way to introduce the $3 subsidy is to re-arrange the initial supply equation with only P on the left-hand side, and then subtract 3 from the right-hand side to obtain the new supply equation ]

3. A consumer whose tastes are expressed by the following utility function U = (2X + 8) (Y + 5)^{1/2}, and who initially holds a = 8 units of "X" and b = 10 units of "Y", goes to a market where the prices Px = 6 and Py = 3 are both determined independently of his/her wishes. [in case you have no calculus background: MU_{x} = 2 (Y + 5)^{1/2} and MU_{y} = (1/2) (2X + 8) (Y + 5)^{-1/2} ]. Please find:

a. The consumer's demand function for good Y [Hint: maximize total utility at the equilibrium point by equating the slope of the indifference curve to the slope of the budget line (do NOT replace P_{x} and P_{y} with their given values for this part of the question); to obtain the demand function for Y, re-arrange the utility-maximizing equation with only XP_{x} on the left-hand side and substitute XP_{x} into the equation of the budget line].

b. The MRS_{xy} at the equilibrium point.

c. The quantity of Y demanded at the equilibrium point (Y^{*}) [Hint: you must calculate "I" (money income) from the initial endowments "a" and "b": I = a P_{x} + b P_{y}].

d. The equation of the Engel curve for good Y [Hint: along the Engel curve, total utility is maximized, so you must start from the utility-maximizing equation in your answer to "a" above; also, recall that along the Engel curve all variables other than Y and I are held constant]. Is Y a normal or an inferior good for this consumer? Why?

e. The equation of the income-consumption curve (ICC) [Hint: along the ICC, total utility is maximized, so you must start from the utility-maximizing equation in your answer to "a" above; also, recall that along the ICC the price ratio is held constant].

End results: (a) Y^{*} = (I -10P_{y} +4P_{x}) / 3P_{y} ; (b) MRS_{xy} = 2

(c) Y^{*} = 8; (d) Y = (I - 6)/9; (e) X = Y + 1

4. Calculate the consumer's equilibrium (X^{*} and Y^{*}) from the following information:

Y - 20 Px = 2

MRS_{xy} = ──────── ; Py = 3

X – 30 I = 40

Subject | Business |

Due By (Pacific Time) | 06/03/2014 06:00 pm |

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