Download Review Sheet for UGBA - Microeconomic Analysis for Business Decisions | UGBA 101A and more Study notes Introduction to Business Management in PDF only on Docsity! Some review for the first UGBA 101A exam Charlie Gibbons∗ University of California, Berkeley September 28, 2007 Elasticities Own price (demand) Dxx = dxD dpx px xD Own price (supply) Sxx = dxS dpx px xS Cross price xy = dx dpy py x Income ηx = dx dI I x Substitution σ = d(KL ) dMRTSL,K MRTSL,K (KL ) Equilibrium conditions Interior solution x, y > 0 MRSx,y = px py Corner solution x > 0, y = 0 MRSx,y > px py x = 0, y > 0 MRSx,y < px py Directions of income and substitution effects of price changes on x Substitution effect Income effect Total effect Normal good Inferior good Normal good Inferior good If px ↑ x ↓ x ↓ x ↑ x ↓ ? If px ↓ x ↑ x ↑ x ↓ x ↑ ? ∗cgibbons@econ.berkeley.edu 1 Consumer and producer analogues Consumers Producers Utility function U(x, y) = U Production function F (L,K) = Q Marginal utility MUx, MUy Marginal product MPL, MPK Indifference curves { (x, y) : U(x, y) = Ū } Isoquants { (L,K) : F (L,K) = Q̄ } Marginal rate of MRSx,y = MUx MUy Marginal rate of MRTSL,K = MPL MPK substitution technical substitution Solving for an equilibrium 1. Set QS = QD and solve for the equilibrium price. 2. Plug the equilibrium price into either QS or QD and solve for the equilibrium quantity. Finding a demand curve for x 1. Solve MRSx,y = px py for y in terms of x. 2. Substitute the expression for y into the budget constraint and solve for x in terms of px. 3. See if there are any values of px such that the demand for x is 0 or negative. In these instances, only y will be consumed (important step for quasi-linear utility). This procedure works if there is an interior solution to the problem. If utility is linear, this will not be the case. Instead, use the corner solution equilibrium conditions listed above to determine whether only x or only y will be consumed. For quasi-linear utility, there will be an interior solution for some values of px, py, and I and this procedure will permit you to identify these values. Finding an optimal consumption bundle 1. Follow the instructions above to find the demand curve for x. 2. Plug in the appropriate values of the exogenous parameters to solve for x. 3. Plug this value of x into the equilibrium condition for the problem to find y. Algebraically identifying income and substitution effects on x 1. Find the optimal bundle under the original prices and income, (x0, y0). Also, calculate the utility of this bundle, U(x0, y0) = U0. 2
