Hi! I really need help with problems 3 & 5. I've attached pictures of the problems and the relevant notes I have from class. I know on number 5 my professor said something about keeping in mind that they're identical twins and using indifference curves.

Firms A and st decide how to set price and whether to undertake product differentiating advertising. The table gives returns to three options, where A is the row player and B is the column player. Payoffs are given as (A payoff, B payoff). Firm B What are all the Nash high p, high p , low p equilibria for these no ad ad firms? (What strategy combinations?) Explain. high p, no ad (50, 50) (38, 60) (40, 45) high p, Firm A ad (60, 38) (45, 45) (43, 47) low p (45, 40) (47, 41) (42, 42) 3. Brad's Bowling Balls, Inc. has the production function Q = 2V KL (here the square root applies to the product of K and L), the competitively established bowling ball price is $30 per ball, and Brad has 25 units of capital. a. Compute Brad's demand for labor, showing how much labor he wants for any given wage. b. Each bowling ball made requires a $10 plastic ball and wax that costs $2. Adjust the deman for labor to incorporate these facts and produce the true demand for labor. 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Create a payoff matrix to represent the game of rock, paper, scissors. Explain the values you put in (you can just use any numbers as long as the relative values make sense). Is there a dominant strategy? Are there any equilibrium strategy combinations? 5. In the late 1800's, many people in the South earned their living by sharecropping. Under this arrangement, the landowner would provide a tenant farmer with land, and possibly necessary tools and animals. In return, the cropper would pay the owner a portion of the crop. The typical farmer had up to 800 hours he could work on a crop, and the expectation was that each additional hour of time spent farming would add $1 to the value of the crop (the farmer's earnings). a. Consider identical twin brothers working under two alternative cropping arrangements. Jacob borrows from the landowner the implements and mule he needs for his tenant farm, so he must pay the landowner half of his crop. In other words, he keeps only half of the earnings from his labor. Esau decided to borrow $50 to buy his own mule and tools, so he pays only 25% of his crop value to the landowner, and he keeps 75% of his crop value. He must, of course, also repay the loan. Draw the budgets for the brothers, carefully. Suppose Jacob works 200 hours per year. Would he be better off switching and imitating Esau? For these brothers, which plan is better, for this one year? b. Now compare the better of the two sharecropping arrangements with the case of another farmer who owns his own land, tools, and mule. This farmer keeps the entire earnings of his farm. If he has the same tastes as Jacob and Esau, will he work more or less than the twin with the better arrangement?short run . _ variable k = capital L= Lauber - Iso Chant Q- 25 G=UP Do - Iso grant = every combination of Capital3 Laber on that carre will produce the Same quantity . they slope down - MP 20 " higher curve means higher out pul KA Isoquants can't intersect Probably have to de prests Q - _ _ JAL = 2 / = KZ on fest is aquant for A = y 7 / 22 AL LK 2/ 2 slope = - y = L .K Q = 4 y 3- extra output from adding AL labor. AL'X MPL - output lost from taking away AK' capital said AK' x MP man k mar Since back on same isoquant, AL x MPL AK'- Mik MP, = AF . MRK tells me the man AL Slope as it AK depends on the margo met AL' products MRTS - Marginal rate of technical Substitution Returns to scale : Scaling upor down all the somaltaneously - if increase all inputs bythe same factor / then . If output by same factor , call it return to scale . If output by a Larger factor, call it increasing its to socable - If intently by a smaller factor it is decreasing RTS - Need anisorost: a curve that cameat all points out he graph that have the somme costC = Cost ofL + cost of to C = wil + rik I K = C - WL k= - with er not move iso quant be ange 12 that's where wants to set the cheapest Combination, can see 3 by seeing what will get us lowest isacost . F- cost minpoint i-where i so cost is tangent to isoquant - on desired iso quant MPL - equal Slopes = ? MP = W = MPK fCar, tall 22 1 =Q you arehere MPK= Iz MPL=18 USOCOST MRt's labor MP stope of isereast 12 MR K I slope of Joquant 2 W MARK W. MPK MPL AAPL M P K . 12 = 2 W spend more on Labor time Q is distance on miles can't go over 60 mph, going spend more tume driving , can't have anything below dotted line, the gas usoCOST Will shift PROVES will to the ewr to right Kielereley costhas increased- The wage affects the labor, not the capital Ko - If the wage rate 0- 27 goes up, Labor endpt. goes to the left's Capital end point stays same - reminiscent of scubstitation effect E17 EIS 4 = 13 2 5 cost of making 13frMRP, = MR- MPP , 18/ 22 fuel for good other goods Slope I- +68w Le 168 Leisure per week - Always want intercepts , slope, equilibrium - Find Labor by fromdifference of intercept ? equilib ( from RotoH ) 09 SE . what if you have a higher wage (w') but 16 0w/ can only reach original FE Lo ESE It- hypothetical, parallel IE 1 to SE L 168 lessure /FR: impact of higher per week real income, more from ormal or inferior ? hypothetical budget toget more leisure, have toberight to new budget of N richer or poorer? compared to point *6. 106 TO 24 leisure per day - wage rate is unaffected , so slope is the samerist part) - blue budget you get by the, Light binesy. so he first one allows for more leisure, no SE