Question

1. (a) Your company has $3000 to spend on widgets and Gadgets. Derive the budget constraint when the per unit costs of Widgets and Gadgets are $10 and $20 respectively. (b) Suppose the per unit price of Widgets goes up to $20, how will the price increase alter the constraint of the company? Show the income and substitution effects after the price change.

Answer 1

Let W be the number of widgets and G be the number of gadgets consumed.

Budget constraint is given by: 10W+20G=3000

If all of the consumer's income is spent on widgets (and none on gadgets), the consumer can buy 3000/10 = 300 widgets.

If all of the consumer's income is spent on gadgets (and none on widgets), the consumer can buy 3000/20 = 150 gadgets

The slope of the budget constraint is given by: -300/150 = -2/1

This means that 2 unit of widgets must be given up in order to afford 1 extra unit of gadget.

b. If the unit price of widgets is $20/unit then budget constraint is given by:

20W+20G=3000

If all of the consumer's income is spent on widgets (and none on gadgets), the consumer can buy 3000/20 = 150 widgets.

If all of the consumer's income is spent on gadgets (and none on widgets), the consumer can buy 3000/20 = 150 gadgets.

The slope of the budget constraint is given by: -150/150 = -1/1

This means that 1 unit of widgets must be given up in order to afford 1 extra unit of gadget.

After an increase in the price of the widget, the consumption of widget has reduced to 150 from 300. There is a decrease in the real income of the company and therefore the consumption of widgets falls due to income effect. The consumption of gadgets remain the same so there is no substituion effect.