Managerial Economics: Lecture 5 Carlos A. Ulibarri Department of Management New Mexico Tech

efficiency loss from decision-making with incomplete information Measured as a welfare loss triangle in the marginal benefit (MB) - marginal cost (MC) diagram. Horizontal axis Q ~ No. of units per day in 1’000s. Vertical axis P ~ dollars per unit ($/Q).

quantity-setting Qnty = Qo based on over-estimate of MC, say E(MC). Allocation decision under incomplete information at point b, on the actual marginal cost curve (MCa). Efficiency loss ∆abc, since MB remains greater than actual marginal cost. See overhead.

Overhead 1

price-setting Price = Po based on overestimate of MC. Allocation decision under incomplete information at point f, on the actual marginal cost curve (MCa). Efficiency loss = ∆cfe, since actual marginal cost exceed marginal benefit. See overhead.

Overhead 2

comparing efficiency of decisions Whether Q or P signaling is most efficient depends on the relative slopes of the MB and MC curves.

decentralized v centralized decision-making under uncertainty HQ Div 1Div 2Div 3 Decentralized decision-making: localized at each division (risk coordination failure?) Centralized decision-making: localized information from each division must be communicated to HQ, where centralized decision is made.

question #1 p. 120 P. Milgrom & J. Roberts Assume division #1 supplies an input to division #2. Division #1 has complete information over its marginal cost =MC1. At division #2 there is incomplete information, i.e. the marginal benefit from using the input is uncertain. What quantity of the input will be produced-used if quantity setting is applied in allocating the input? What quantity of the input will be produced-used if price setting is applied in allocating the input?

underestimation of marginal benefit Under qnty-setting at Qo division #1 supplies Qo units of the input at marginal cost MC1. Division #2 uses the input at expected marginal benefits E(MB)= MC1. Efficiency loss = ∆abc since actual MB ≥ MC1. Under price-setting at Po, division #1 supplies Q2 units of the input at marginal cost MC2. Division #2 uses this quantity of the input, resulting in an efficiency loss = ∆ade, since actual MB ≤ MC2.

Overhead 3

break

product launch Q#2, p. 120 Milgrom and Roberts New product introduced in competition with another form. HQ estimates there is 1 st mover advantage, as represented by “winner-take-all” profits:

3 divisions must coordinate Div #1: ABQ & Socorro Dept A (mfg component) Div #2: Socorro Dept B (mfg finished product) Div #3: All other off-site Depts. (transport/distribute) Each division incurs sunk costs preparing for launch: C1=3(12-t) C2=4(12-t) C3=5(12-t)

questions 1. What is the optimal launch time and corresponding level of net profits? 2. What are your divisions’ sunk costs? 3. What will be the firm’s level of net profits if divisions 1 and 3 meet the optimal target date, while division 2 is pushed into being ready one month beforehand?

Questions cont. 4. Does a small timing error in division 2 yield a larger loss than a centralized timing error of the same magnitude (e.g. t= 5 instead of t*=6)?