We Love Econs

★ We Love Econs! ★ Econs uses a lot of graphs, which is actually math in pictures. But going straight to the math is often clearer, cleaner, and faster to present in essays.

★The Demand Curve We get happiness from consumption. Each ice cream, for instance, makes us happier. But the 10th ice cream brings less happiness than the 1st one because we get sick of ice cream after awhile. We can plot happiness (H) (y-axis) against units of ice cream (q) (x-axis) to get a curve that is H

-

dH d 2H > 0 < 0. Upward sloping: & getting more gentle: dq dq 2

q

This graph can be described by the equation H = q .

Lets say H is measured in units of money ($). So the profit you get from eating ice cream is simply your total happiness – cost of the ice cream. - Mathematically, profit = H – C =

q − qP . (qP = no. of ice creams x its price)

- To find the maximum profit we differentiate the profit equation:

- Rearranging, P = −

1 q

d ( profit ) 1 =− −P=0 dq q

 which is a downward sloping curve of P against q.

This downward sloping curve is your demand curve! No need for cumbersome ‘effective demand laws’ and such, all we did was to play around with some numbers!

★The Supply Curve

We do the same to obtain the supply curve – differentiate the firm’s profit = revenue – cost. - Revenue = Money from selling ice-cream = qP

-

Cost = q2 because of the Law of Diminishing Marginal Returns (gets increasingly expensive to produce the next unit of output). Profit = qP - q2

Doing the differentiation again we get

d ( profit ) = P − 2q = 0 . dq

Rearranging, 2q = P  the upward sloping supply curve. To find the resultant price and quantity we find the intersection between the two curves. BUT, The supply curve we derived applies only for perfect competition, where P doesn’t change when q changes. This is ok because for DD & SS we assume perfect competition. What happens if there is a monopoly? Facts: -

d (revenue) = Marginal Revenue (MR) dq

-

d (cos t ) = Marginal Cost (MC) dq

Since Profit = Revenue – Cost,

d ( profit ) d (revenue) d (cos t ) = = MR – MC = 0 dq dq dq Therefore we get MR = MC. There! No need lengthy explanations of “the cost of next unit of output must equate to the revenue…”.

In Summary: ★Consumer - Profit = Happiness – Cost = - Differentiating, P = −

1 q

q − qP .  Downward sloping Demand Curve.

★Perfectly Competitive Firm - Profit = Revenue – Cost = qP - q2 - Differentiating, 2q = P  Upward sloping Supply Curve. ★Monopoly - Profit = Revenue – Cost -

d ( profit ) d (revenue) d (cos t ) =  MR = MC dq dq dq

★Elasticity We know that the elasticity of demand =

-

-

% ∆Q where ∆ means ‘change in’. % ∆P

∆Q × 100% Q ∆Q P = . Rewriting, we get ∆P Q ∆P × 100% P ∆Q P . . Rearranging we get ∆P Q 1/(Slope of the demand curve)

Values of P & Q taken from the ‘location’ on the curve, the coordinates (P,Q).

This nicely explains: i) Why a steep curve is more inelastic (because the slope is steeper, and the inverse value is smaller) ii) Why the elasticity as you move to the right of the curve (Q gets larger) gets smaller (as Q increases P falls, and P/Q falls).

In summary, Elasticity of demand =

∆Q P 1 P . = . . ∆P Q slope Q

★Multiplier Effect (National Income Determination) - Like demand & supply, the national equilibrium occurs when: National demand = National supply In other words, AE = Y - We also know that AE is made up of 5 components: AE = C + G + I + X – M. - Of these, C and M are dependent on Y. - C is spending out of disposable income (income less taxes): C = a + b(1-t)Y - M depends on income: M = mY Put C & M into AE = a + b(1-t)Y + G + I + X – mY: - AE = Y  Y = a + G + I + X + b(1-t)Y – mY (1-b(1-t)+m)Y = a + G + I + X 

Y=

1 (a + G + I + X ) 1 − b(1 − t ) + m

1 1 is our multiplier! If G, I, or X increases by 1 unit, Y rises by . 1 − b(1 − t ) + m 1 − b(1 − t ) + m Furthermore, 0 < t < 1, 0 < 1-t < 1 0 < b < 1  0 < b(1-t) < 1 0<m<1 0 < 1 – b(1-t) < 1

0 < 1-b(1-t)+m < 1

1 >1 1 − b(1 − t ) + m 1 A one unit increase in G, I or X causes a rise in Y which is a more than 1 − b(1 − t ) + m proportionate rise in Y. There is thus no need for tedious tables and explanations of the multiplier in your exams, just present these steps: Y = AE = C + G + I + X – M Y = a + G + I + X + b(1-t)Y – mY 1 Y= (a + G + I + X ) 1 − b(1 − t ) + m 

1 is the multiplier and is greater than 1. 1 − b(1 − t ) + m