# Project #32362 - Assigment 1

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:  Xs = -6 + 2P  and  D:  Xd = 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: MUx = 2 (Y + 5)1/2 and MUy = (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 Px and Py 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 XPx on the left-hand side and substitute XPx into the equation of the budget line].

b.         The MRSxy 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 Px + b Py].

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 -10Py +4Px) / 3Py ;               (b) MRSxy = 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

MRSxy =    ;                     Py = 3

X – 30                         I  = 40

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