Sunday 13 June 2010

Economics -- Price elasticity and Government intervention (rearranged)

The price elasticity of demand/supply (Ed/Es) refers to the responsiveness of the Qd/Qs to a price change.

Ed = %ΔQd/%ΔP and Es = %ΔQs/%ΔP where %ΔX = (X2-X1))/[(X1+X2)/2]*100%.

Elasticity only refers to the magnitude of Ed/Es only. Ed<0 since P and Qd is negatively related. Note that the elasticity refers to % change rather than absolute difference.

Types of elasticity:
  1. Perfectly inelastic (Ed / Es =0) if %ΔQd / Qs=0, i.e., remains unchanged for a change in price. Its curve is vertical.
  2. Inelastic (0<Ed / Es <1)%ΔQd / Qs<%ΔP, its slope it somehow straight.
  3. Unitarily elastic: (Ed / Es =1) %ΔQd / Qs=%ΔP, it forms a rectangular hyperbola
  4. Elastic: (1<Ed / Es <∞) %ΔQ / Qs>%ΔP, the slope is somehow flat.
  5. Perfectly elastic: (Ed / Es =∞), where %ΔP0 causing an infinitely large change in Qd/Qs.. Its slope is horizontal.
In a free market, TR of firm = TE of buyers = Total exchange value = PQd.

When Ed>1, PTR, PTR when Ed<1 and TR remains unchanged neglecting the chance of P if Ed=1.

Note that when the curve is linear, the mid-point between the intersection with x-axis and y-axis will have Ed=1, the part above that point will have Ed>1 and the part below the point will have Ed<1. We can proof this one by considering TR maximized at the midpoint.

Factors affecting the price elasticity of demand:
  1. Closer substitutes available→more elastic
  2. Demand of necessities→more inelastic, demand for luxuries→more elastic
  3. Consumption habits: harder to change the habit→more inelastic
  4. Proportion of expenditure to income↑ → more elastic
  5. Price range↑ / More useful / More durable → more elastic
Factors affecting the price elasticity of supply:
  1. Nature of goods, e.g. land, artworks of deceased painters will be perfectly inelastic.
  2. Flexibility of production: ease of adjusting production (e.g. faster training to unskilled workers)↑→Es↑.
  3. Factor mobility ↑→Es↑
  4. Reserve capacity (Max. amount of resources that can be put into production)↑→Es↑
  5. Time allowed to adjust production↑→Es↑
  6. Lower entrance to the industry→Es↑
Market intervention
  1. Price ceiling / Max price control: Under this condition, producers/sellers are not allowed to charge more than the max price. (e.g. rent control of residential units before 1999 in HK). Effective price ceiling P’<Pe, otherwise the equilibrium point is still at the interception point of the demand curve and supply curve. In this case a shortage appeared where the quantity transected refers to the intersection of supple curve and the price ceiling. In this case P’<P, Q’<Q, new TR = P’Q’<PQ=original TR. In this case price failed to allocate resources, so non-price competition arises such as queuing, drawing lots, by needs, etc. Black market will also arise. Graphically the price of black market will be the vertical projection of the new quantity transected to the demand curve.
  2. Price floor / Min price control: Under this condition the consumers/buyers are not allowed to pay less than the minimum price. (e.g.: min wage to the foreign domestic helpers) The price floor is effective only if P’>P0. In this case the new quantity transected will be the intersection between demand curve and the price floor. As the new point is on the demand cure, P’>Pe but Q’<Q0. We check the change of TR by the price elasticity of (original) demand: if Ed<1, TR↑, if Ed>1, TR↓, Ed=1, TR unchanged. In this case surplus appeared and sellers compete to sell products. Since they can’t cut the price, they competes by non-price competition such as free gifts and improve their skills. Some even cut their price illegally (to the vertical projection of the new quantity transected to the supply curve) to eliminate excess supply.
  3. Quantity control / quota: It is the maximum amount of output. (e.g. # of taxis and minibus in HK) Effective quota implies that the Q’<Qe. Graphically the supply curve was bent into a vertical line at the quota. The new quantity transected will be the intersection between the new supply curve and the demand curve. In this case P’>Pe and Q’<Qe so we check the TR by considering the price elasticity of the demand just same as the price floor. Since the sellers can’t sell more in quantity, they improve the quality which gives them a higher TR.
  4. Unit tax: same amount of tax imposed to every unit of product (different from valorem tax which the tax refers to a % of the price) (e.g., unit tax on petrol) In this case the supply curve shifts upwards by the amount of tax. In this case P’>Pe and Q’>Qe, and the part of the TR (Tax*Q’) will be the tax given out. For the consumers the burden will be (P’-Pe)*Q’ while the producer’s burden will be the remaining part (Tax-P’+Pe)*Q’. After the tax is imposed the TR is reduced by (Tax*Q’+(Qe-Q’)*Pe. The second of TR loss was due to the shift on demand curve. The TE of consumers refers to the elasticity of the demand curve like the previous intervention. The distribution of tax burden can also be given from the formula:
Consumer’s tax burden/producer’s tax burden = Es/Ed.
  1. Unit subsidy: A same amount of subsidy is granted to each unit of output.
(e.g., government schools). In this case the supply curve shifts downwards by the amount of unit subsidy. The new equilibrium will be the intersection between the new supply curve and demand curve. In this case P’<Pe and Q’>Qe. We find the change in TE by considering the price elasticity of demand curve like the previous cases. The total subsidy will be Tax*Q’. In this case the consumers’ share on the unit subsidy will be Q’*(Pe-P’) while the producers get the remaining part of subsidy, that is, Q’(Tax-Pe+P’). Therefore the new TR of the producers will be Q’(2P’+Tax-Pe). The distribution of unit subsidy can be given by:

Consumer’s share of subsidy / producer’s share subsidy = Es/Ed.

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