Question

4. A consumer has 10 pounds of gold and 20 pounds of silver. The price of gold ?) = $4,000 a pound while the price of silver ?* = $1,000 a pound. Gold and silver are the only two goods that can be consumed.

   1. Write down the budget constraint of this consumer and draw it on a graph.

   2. Suppose that the price of silver increases to $2,000 a pound. Draw the new budget

      constraint. Has the purchasing power of our consumer increased or decreased?

   3. Assume that the tastes of the consumer can be represented as ? = ???(?,?), where ? is the quantity of gold consumed and ? is the quantity of silver consumed. Is he better

      off in (a) or in (b)? What if his preferences are represented as ? = ??? (?, 3?)?

Answer 1

Quantity of gold q=10 pounds

Quantity of silver q*=  20 pounds

The price of gold ? = $4,000 a pound

The price of silver ?* = $1,000 a pound

Let, Total money income=M

The budget constraint will be ,

pq+p^*q^* = M

Putting the values of p ,q ,?*, q* we get

10*4,000+20*1000=M

M=60,000

4,000q+1000q*=60,000

q/15+q*/60=1

The price of silver increases to $2,000 a pound

The new budget constraint is ,

10*4,000+20*2000=M

M=80,000

4,000q+2000q*=60,000

q/15+q*/30=1

Due to increase in the price of silver the maximum amount of silver the consumer can buy is 30 pound. Previously it was 60 pound. After increase in the price of silver consumer's real inncome falls.so the purchasing power decrease.