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4. Two producers can grow food for a consumer who cares only about food and money. Producer 3' (j = 1,2) can plant qj > 0 units of seed at a cost of (1/3) + qj (in units, of money) and then produce qj units of food from the seed at no additional cost. If a producer plants no seed, it has no cost. The agents' interaction can be described as a game in which the producers independently plant qj 2 0 units and pay any cost of planting. Next, they independently choose food prices p;- 2 {l (in terms of money) and then the consumer chooses to buy (25- E [0, 93] units of food from each producer j. The payoff of producer 3' is its revenue pjcj minus its cost. (It, can borrow to pay for seed at no interest and repay its loan from its revenue.) The consumer's payoff is So (1/2)c2 plcl 1:92:22, where c = cl + 02. All this information is common knowledge. a. How many pure strategies does the consumer have? Give an example of one. b. Show that in the consumer's best response to (Q1, qg, pl, 192), if p1 D and {12 > 0. c. Show that there is no pure subgame perfect equilibrium (SPE) of this subgame in which p1 <: and> 0. Hint: Use part b and consider deviation by producer I. d. Use parts b and c to show that this subgame has no pure SPE of this subgame in which 0