In the questions 16-18 use these values in the multivariate demand function for Grapple tablets: PR = $500 Ph= $600 Pr = $600 Pav = $50 Pac = $100 Pmm = $30 Ag = 40 A = $100,000 C =2 Y=$30,000 16. After the values above are entered into your demand function, what quantity of Grapple tablets will be demanded? Be very careful with this calculation. This value will be used again below. 17. What is the point cross-price elasticity of Grapple tablets at the above price of Hewpaq laptops (P)? Show the values you use in the formula and work out completely. Be sure to show the sign. Does this value indicate a very sensitive (elastic; responsive) relationship (write a one sentence comment)? The formula is: E = OP Q , 18. What is the point age elasticity of Grapple tablets at the above age level (A.)? Show the values you use in the formula and work out completely. Be sure to show the sign. Does this value indicate a very sensitive (elastic; responsive) relationship (write a one sentence comment)? The formula is: Q, Ag E = DA Q ,. Consider the following duopoly industry. Demand is given by p = a - 191', where p is price, and Y = y1 + y: is market quantity. y; represents the amount produced by rm i. The two firms have the same marginal cost equal to c. Assume a is large enough and there is no xed cost. (50 points) (1) In a Cournot model (two rms decide their output levels simultaneously and independently), solve each rm's Output quantity and prot, market price, and market quantity. (2) Now suppose two rms collude to decide their output levels together and split the market demand equally. Solve each rm's output quantity and prot, market price, and market quantity. (3) Now suppose two rms move sequentially and firm 1 is the leader (Stackelberg model). Solve each firm's output quantity and prot, market price, and market quantity. (4) Put your results 'om the previous three sub-questions in the following table. -_-__-\"\" Com ------ Collusion Stackelberg Model (5) Compare your results and explain. (Cournot vs. Collusion and Cournot vs. Stackelberg) 3. Consider the following delegation versus centralisation model of decision making, loosely based on some of the discussion in class. A principal wishes to implement a decision that has to be a number between 0 and 1; that is, a decision d needs to be implemented where 0 S d S 1. The difculty for the principal is that she does not know what decision is appropriate given the current state of the economy, but she would like to implement a decision that exactly equals what is required given the state of the economy. In other words, if the economy is in state s (where 0 S s s 1) the principal would like to implement a decision d = s as the principal's utility Up (or loss 'om the maximum possible prot) is given by UP = is d | . With such a utility mction, maximising utility really means making the loss as small as possible. For simplicity, the two possible levels of s are 0.4 and 0.7, and each occurs with probability 0.5. There are two division managers A and B who each have their own biases. Manager A always wants a decision of 0.4 to be implemented, and incurs a disutility UA that is increasing the further from 0.4 the decision d that is actually implement, specically, U A = 'OA d|. Similarly, Manager B always wants a decision of 0.7 to be implement, and incurs a disutility UB that is (linearly) increasing in the distance between 0.7 and the actually decision that is implemented - that is U B = |0.7 d l . Each manager is completely informed, so that each of them knows exactly what the state of the economy 5 is. 1. Evan can grow both roses and carnations in his garden. His production possibility table is given below. If he is currently producing 110 roses, his opportunity cost of producing 40 more roses is: Number Number of roses of carnations 155 60 135 110 109 150 78 180 0 A. 20 carnations. B. 26 carnations. C. 31 carnations. D. 78 carnations. 2. Because you can only get more of one good by giving up some of another good, the shape of a production possibilities curve is: A. upward sloping. B. perfectly vertical. C. perfectly horizontal. D. downward sloping. AC 30 20 10 20 Eggs