Chapter 10, Problem 10.10P

a)

To determine

The Edgeworth box diagram for all possible exchange in given situation is to be drawn and the contract curve for this exchange economy is to be described.

Answer to Problem 10.10P

Any point off the contractcurve is inefficient.

There is possibility to increase welfare by reallocating the resources.

Curve J indicates the indifference curve of consumer 2, and the slope of the curve is equal to -3/4

Instead, the consumer 1 indifference curve is indicated by the S with slope -1/2.

Explanation of Solution

Consumer 1selects two slices of cheese to each slice of ham.

Thus, the contract curve would be astraight line and any allocation outside the line would be inefficient.

Consumer 2 would enter into the exchange where the exchange ratio is less than the four cheese slices forthe three ham slices.

The following is the Edgeworth box diagram:

  

Both consumers have been shown in the Edgeworth box diagram.

Equilibriumisrecognizedat the indifference curves of both consumers tangent.

Any point off the contractcurve is inefficient.

There is possibility to rise welfare by reallocating the resources.

Curve J shows the indifference curve of consumer 2, and the slope of the curve is equal to -3/4.

Instead, the consumer 1 indifference curve is indicated by the S with slope -1/2.

Economics Concept Introduction

Introduction:Edgeworth box is a way of representing various distribution of resources

In contract curve can be explained as a set of points shows final allocation of two products among two individuals that could arise as a result of mutually beneficial trading among those individuals given their initial allocation of the products.

b)

To determine

considering consumer 1 initial endowment is 40 slices of ham and 80 slices of cheese. Manual beneficial treads possible in this economy are to be described and utility levels of both the consumers enjoy from trades are to be described.

Answer to Problem 10.10P

There would not be any exchange, as allocation is already efficient.

Explanation of Solution

Consumer 1 initially had 40H and 80C, and Consumer 2 initially had 60H and 120C.

The following isthe total utility of consumer 2:

  $60\times 4+120\times 3=600$

The above equation can be written as

Utility of consumer 2

  $=4H+3C=600$

And

  $C=2H$   .............(2)

Adding the value of equation (2) in equation (1),

Utility of Consumer 2

  $\begin{array}{l}=4H+3\left(2H\right)=600\\ =4H+6H=600\end{array}$

Utility of Consumer 2

  $\begin{array}{l} =4H+3\left(2H\right)=600\\ =4H+6H=600\\ =10H=600\\ H=\frac{600}{10}\\ =60\end{array}$

Substituting the value of H in equation (2)

  $\begin{array}{l}C=2H\\ =2\times 60\\ =120\end{array}$

There would not be any exchange, as allocation is already efficient.

Economics Concept Introduction

Introduction: Utility function refers to define individual priority for products or services beyond the monetary value of those goods or services.

c)

To determine

Considering that 20 slices of ham could be transferred without cost fromconsumer 2 to consumer 1 endowmentUtility level of both the consumers is to be described.

Answer to Problem 10.10P

A trade exchange will take place in such a situation, and 16 ham slices would be exchanged for 8slices of cheese.

Explanation of Solution

Consumer 2 transfers the 20 slices of ham to Consumer 1, and now Consumer 2 has 40H and 120C.

Thefollowing is the total utility of consumer 2:

  $40\times 4+120\times 3=520$

The above equation can be written as follows:

Utility of Consumer 2

  $=4H+3C=520$

And

  $C=2H$

Utility of Consumer 2

  $\begin{array}{l} =4H+3\left(2H\right)=520\\ =4H+6H=520\\ =10H=520\\ H=\frac{520}{10}\\ =52\end{array}$

Substituting the value of H in equation (2),

  $\begin{array}{l}C=2H\\ =2\times 52\\ =104\end{array}$

A trade exchange will take place in such a situation, and 16 ham slices would be exchanged for 8slices of cheese.

Economics Concept Introduction

Introduction: Utility function refers to define individual priority for products or services beyond the monetary value of those goods or services.

d)

To determine

Consumer 2 transfer ham and consumer 2 carries through on her threat then mutually beneficial trades are to be described and utility level of both consumers are to be described.

Answer to Problem 10.10P

It would enhance the welfare of the both.

Explanation of Solution

Consumer 2 objects to the transfer of ham that is proposed. Consumer 2 is ready to throw out the haminstead of giving it to Consumer 1.

Such an incident would reduce overall welfare. Instead ofthrowing out the ham, they can both come to the negotiating table and share it.

It would enhance the welfare of both.

Economics Concept Introduction

Introduction: Utility function refers to define individual priority for products or services beyond the monetary value of those goods or services.

e)

To determine

Consumer 1 expect ham transfer from the consumer 2 and allow 20 slices of her initial ham endowment to spoil. Considering transfer from joined actually happens, mutual trades are to be described and potential utility level for both consumers is to be described.

Answer to Problem 10.10P

At the efficient level of allocation, Consumer 2 has 48 ham slices and 96 cheese slices.

Explanation of Solution

The following would be the utility function of Consumer 2 after the spoilage.

Consumer 2 suffers the loss ofa total of 40 ham slices (20 to spoilage and 20 to transfer):

  $60\times 4+80\times 3=480$

The above equation can be written as follows:

Utility of consumer 2

  $\begin{array}{l}4H+3C=480\\ And\\ C=2H\end{array}$

Utility of Consumer 2

  $\begin{array}{l} =4H+3\left(2H\right)=480\\ =4H+6H=480\\ =10H-480\\ H=\frac{480}{10}\\ =48\end{array}$

Substituting the value of H in equation (2),

  $\begin{array}{l}C=2H\\ =2\times 48\\ =96\end{array}$

At the efficient level of allocation, Consumer 2 has 48 ham slices and 96 cheese slices.

Economics Concept Introduction

Introduction:

Utility function refers to define individual priority for products or services beyond the monetary value of those goods or services.

f)

To determine

considering that both of the adverse incentive effects mentioned in part d and c occurs simultaneously then mutual beneficial treading opportunity remain and potential utility levels for both consumers is to be described.

Answer to Problem 10.10P

consumer 2 has 42 slice of hams and 84 slices of cheese. Alternatively, Consumer 1 has 58

slices of ham and 96 slices of cheese.

Explanation of Solution

When both conditionsoccurconcurrently, the total loss of ham is 60; Thusnow Consumer 2 has only60 ham slices (20 thrown out +20 spoilage +20 transfers).

The following would be the newutility function:

  $60\times 4+60\times 3=420$

The above equation can be written as follows:

Utility of Consumer 2

  $\begin{array}{l}=4H+3C=420\\ And\\ C=2H\end{array}$

Utility of Consumer 2

  $\begin{array}{l}=4H+3\left(2H\right)=420\\ =4H+6H=420\\ =10H=420\\ H=\frac{420}{10}\\ =42\end{array}$

Substituting the value of H in equation (2)

  $\begin{array}{l}C=2H\\ =2\times 42\\ =84\end{array}$

Here, consumer 2 has 42 slices of hams and 84 slices of cheese. Alternatively, Consumer 1 has 58

slices of ham and 96 slices of cheese.

Economics Concept Introduction

Introduction: Utility function refers to define individual priority for products or services beyond the monetary value of those goods or services.