Two players (1 and 2) take turns putting pennies inside a jar. Each player can place no less than one and no more than three pennies in the jar at each turn, that is, a player can put one penny, or two, or three, and then the other player takes her turn. Players stop when the number of pennies in the jar reaches 13. The jar is empty at the beginning of the game and player 1 starts first. The player that puts the 13-th penny in the jar wins and the other loses. Players only care about winning, that is, being the player that puts the 16-th penny in the jar, and are indifferent among all terminal histories that they win; or among all the terminal histories where they ose -) Required:
Let m, 0 <= m <=16, be the number of pennies in backwards the jar before player i takes her turn but without explicitly solving for an SPNE, determine for what values of m does the player whose turn is to move win?

Exercise 18-15 sheffield appliance center is an experienced home appliance dealer. sheffield appliance center also offers a number of services for the home appliances that it sells. assume that sheffield appliance center sells ovens on a standalone basis. sheffield appliance center also sells installation services and maintenance services for ovens. however, sheffield appliance center does not offer installation or maintenance services to customers who buy ovens from other vendors. pricing for ovens is as follows. oven only $790 oven with installation service 850 oven with maintenance services 970 oven with installation and maintenance services 990 in each instance in which maintenance services are provided, the maintenance service is separately priced within the arrangement at $180. additionally, the incremental amount charged by sheffield appliance center for installation approximates the amount charged by independent third parties. ovens are sold subject to a general right of return. if a customer purchases an oven with installation and/or maintenance services, in the event sheffield appliance center does not complete the service satisfactorily, the customer is only entitled to a refund of the portion of the fee that exceeds $790. assume that a customer purchases an oven with both installation and maintenance services for $990. (b) indicate the amount of revenue that should be allocated to the oven, the installation, and to the maintenance contract.

Suppose that electricity producers create a negative externality equal to $5 per unit. further suppose that the government imposes a $5 per-unit tax on the producers. what is the relationship between the after-tax equilibrium quantity and the socially optimal quantity of electricity to be produced?

Suppose the government enacts a stimulus program composed of $600 billion of new government spending and $300 billion of tax cuts for an economy currently producing a gdp of $14 comma 000 billion. if all of the new spending occurs in the current year and the government expenditure multiplier is 1.5, the expenditure portion of the stimulus package will add nothing percentage points of extra growth to the economy. (round your response to two decimal places.)