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Econ 150 Problem Set 7

# Econ 150 Problem Set 7 - 1 Question 1 a Part a i...

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1. Question 1 a. Part a i. Calculations 1. If firm #1 produces q n = 2/3 x 10 8 and firm #2 produces q c = 5 x 10 7 a. ( 29 2 1 7 10 * 2 1 11 q q P + - = - b. ( 29 7 8 7 10 * 5 10 * 3 2 10 * 2 1 11 + - = - P c. 6 31 = P d. ( 29 ( 29 ( 29 M q MC P PS 278 10 * 3 2 1 6 31 8 1 1 = - = - = e. ( 29 ( 29 ( 29 M q MC P PS 208 10 * 5 1 6 31 7 2 2 = - = - = 2. If firm #1 produces q n = 7.5 x 10 7 and firm #2 produces q n = 2/3 x 10 8 a. ) ( 10 * 2 1 11 2 1 7 q q P + - = - b. ( 29 8 7 7 10 * 3 2 10 * 5 . 7 10 * 2 1 11 + - = - P c. 12 47 = P d. ( 29 ( 29 ( 29 M q MC P PS 219 10 * 5 . 7 1 12 47 7 1 1 = - = - = e. ( 29 ( 29 ( 29 M q MC P PS 194 10 * 3 2 1 12 47 8 2 2 = - = - = 3. If both firms produce q n = 7.5 x 10 7 a. ) ( 10 * 2 1 11 2 1 7 q q P + - = - b. ( 29 7 7 7 10 * 5 . 7 10 * 5 . 7 10 * 2 1 11 + - = - P c. 5 . 3 = P d. ( 29 ( 29 ( 29 M q MC P PS PS 188 10 * 5 . 7 1 5 . 3 8 1 2 1 = - = - = = ii. Matrix (all values to the nearest million) 1. M M M M M M q M M M M M M q M M M M M M q q q q h n c h n c 188 , 188 194 , 219 188 , 281 219 , 194 222 , 222 208 , 278 281 , 188 278 , 208 250 , 250 b. If firm #2 produces q c , firm #1’s optimal production level is q h ; if firm #2 produces q n , firm #1’s optimal production level is q n ; if firm #2 produces q h , firm #1’s optimal production level is q n . Because there is no single production level for firm #1 that is optimal regardless of firm’s #2’s production level, there is no dominant strategy. c. Since q c is never the optimal production level for firm #1 at any production level for firm #2, firm #1 will never produce at q c . Because firm #1 and firm #2 are symmetric, firm #2 will never produce at q c either. Thus, neither firm will ever produce q c .

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d. If firm #2 produces q n , firm #1’s optimal production level is q n ; if firm #2 produces q h , firm #1’s optimal production level is q n . Since q n is the optimal strategy for each firm regardless of the other firm’s behavior, it is the dominant strategy. e. Profits at q h ,q c are \$281M for the deviating firm; profits at q n , q n are \$222M for both firms; profts at q c , q c are \$250M for both firms. i. The net present value of adhering to the collusive agreement forever 1. ( 29 r r r r r r t t 1 * 250 1 250 1 1 1 250 250 * 1 1 0 + = + = + - = + = ii. The net present value of deviating from the collusive agreement in the first period (the ideal time to do so because of the diminishing present value of future profits) 1. ( 29 r r r r t t 222 281 222 1 * 222 281 222 * 1 1 281 1 + = - + + = + + = iii. The firm will stick to the collusive agreement if the net present value of the profits from adhering to the agreement exceed those of breaking it 1. r
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Econ 150 Problem Set 7 - 1 Question 1 a Part a i...

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