Question

Alter the Diamond-Dybvig model in the following way. Suppose that there are two assets, an illiquid asset that returns 1+r units of consumption goods in period 2 for each unit invested in period 0, and a liquid asset that returns one unit of consumption goods in period 1 for each unit invested in period 0. The illiquid asset production technology cannot be interrupted in period 1. The model is otherwise the same as in class. a. Determine a consumers lifetime budget constraint when there is no bank, show this in a diagram, and determine the consumer's optimal consumption when an early consumer and when a late consumer in the diagram. b. Determine a bank's lifetime budget constraint, show this in your diagram, and determine the optimal deposit contract for the bank in the diagram Are consumers who deposit in the bank better off than in part (a)? Explain why or why not. Is there a bank run equilibrium? Explain why or why not. c.

Answer 1

Consumer lifetime Budget Constraint :

let's define a few terms first

M is represent Money income measured in dollars

X = Units of good x

Y = Units of good y

Px = is going to be the price of good x

Py = is going to be the price of good y

So our basic constraints is look like this consumer has a certain amount of money income M that can be spent on good acts and good y this right here is just total spending on X total spending on good X this right here is total spending on good wide price times the quantity purchased total spending on y when we do our budget constraints graphically we"ll we're measuring units here there are physical units goods x physical units of good y so to get an equation that describes a budget constraints. We want to solve this for Y.

M = Px X + Py Y

PX   X ---> total spending on X

Py   Y = M - Px X

So just moving this price times X term over to the other side

Y = M/Py - Px/Py

Expression for the Budget constraints the vertical intercept is right here just take your money income and divide it by the price of good y that's be the maximum number of units of good y that you can buy this is gonna be a downwards sloping line notice the slope just reflects the ratio of the two prices minus the ratio of the two prices so the prices of good x divided by the price of good y. These are basic idea of the budget constraints

wslope = - Px >

Slope line is known as the budget line since it represents the various amounts the consumer can buy with his income : it is also known as price -ratio line or simply the price line.

Consumer's optimal Consumption at Early Consumer and late Consumer

consumer's optimal consumption is a group of indifference curves for two commodities showing different levels of satisfaction. In this indifference optimal consumption it should be clearly understood that a higher indifference curve denotes higher level of satisfaction and a lower indifference curve represents lower level of satisfaction. Being rational, the consumer will always choose a higher indifference curve to get maximum satisfaction other things being equal.

TC+ IC3 g IC, 1 Good x +

1. Indifference curves slope downwards to the right
2. Indifference curves are convex to the Origin
3. No two indifference curves can ever cut each other.

The consumer gets the maximum possible satisfaction from his given income at point C on the indifference curve I3 . At this point, he buys a combination of OX1 amount of good X and OY1 amount of good Y. Any other possible combination of the two goods will either yield lesser satisfaction or will not be unobtainable at present prices, with the given amount of income of the consumer.

Example of Consumer's consumption Budget constraints - X, HOM Good

At the point of equilibrium (point C) the price - line LM is tangential to the indifference curve I3 . At point C, the indifference curve and the price line have the same slope. Now the slope of the indifference curve represents the marginal rate of substitution , and the budget line shows the ratio of prices between the two goods. At point C the marginal rate substitution between the two goods as indicated by the slope of the indifference curve I3 and the ratio of prices between the two goods as indicated by the prices line LM are equal. This point, therefore, indicates the ideal combination between the two commodities, giving the consumer the highest satisfaction possible with his limited income. At this point, therefore the consumer is in equilibrium. The fundamental condition of equilibrium is that the marginal rate of substitution of commodity X for commodity Y should be equal to the ratio of prices between the two goods. Therefore, the condition for equilibrium is MRS = Px/ Py.