4. (20 points) suppose the market demand function is given by (d(p_d) = 60 - p_d) and (s(p_s) = 2p_s).

(a) (5 points) find the market equilibrium without taxes (that is, when (p_d = p_s)).
(b) (5 points) suppose now the supplier is required to pay a per unit tax of (t = 3). draw a graph to show the change in the supply curve. find the equilibrium quantity and prices, (q^*), (p_s^*), and (p_d^*). how much of the per unit tax is passed on to the consumer? (hint: in this case, the vertical axis is the demand price.)

(c) (5 points) suppose now the demander is required to pay a per unit tax of (t = 3). draw a graph to show the change in the demand curve. find the equilibrium quantity and prices, (q^*), (p_s^*), and (p_d^*). (hint: in this case, the vertical axis is the supply price.) compare your answers in parts b and c.
(d) (5 points) calculate the change in consumers surplus, change in producers surplus, tax revenue, and deadweight loss as a result of the policy change. illustrate them on a graph.

Question

4. (20 points) suppose the market demand function is given by (d(p_d) = 60 - p_d) and (s(p_s) = 2p_s).

(a) (5 points) find the market equilibrium without taxes (that is, when (p_d = p_s)).
(b) (5 points) suppose now the supplier is required to pay a per unit tax of (t = 3). draw a graph to show the change in the supply curve. find the equilibrium quantity and prices, (q^*), (p_s^*), and (p_d^*). how much of the per unit tax is passed on to the consumer? (hint: in this case, the vertical axis is the demand price.)

(c) (5 points) suppose now the demander is required to pay a per unit tax of (t = 3). draw a graph to show the change in the demand curve. find the equilibrium quantity and prices, (q^*), (p_s^*), and (p_d^*). (hint: in this case, the vertical axis is the supply price.) compare your answers in parts b and c.
(d) (5 points) calculate the change in consumers surplus, change in producers surplus, tax revenue, and deadweight loss as a result of the policy change. illustrate them on a graph.

Accepted Answer

{ "quality": "clear", "question_count": 4, "skills_matched": [ "step_cot", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": true, "concepts_used": [ "Market Equilibrium", "Tax Incidence", "Deadweight Loss", "Welfare Analysis" ], "new_concepts": [], "current_concepts": [ "Market Equilibrium", "Tax Incidence", "Deadweight Loss", "Welfare Analysis" ] } ## Find the market equilibrium without taxes Using the *Market Equilibrium* knowledge point $$ \begin{aligned} &Q_D = 60 - P,\quad Q_S = 2P\ &60 - P = 2P \implies 3P = 60 \implies P^* = 20\ &Q^* = 2(20) = 40 \end{aligned} $$ ## Analyze tax on supplier Using the *Tax Incidence* knowledge point $$ \begin{aligned} &P_D = P_S + 3\ &60 - P_D = 2P_S \implies 60 - (P_S + 3) = 2P_S \implies 57 = 3P_S\ &P_S^* = 19,\quad P_D^* = 22,\quad q^* = 2(19) = 38\ &\text{Tax passed to consumer} = P_D^* - P^* = 22 - 20 = 2 \end{aligned} $$ ## Analyze tax on demander Using the *Tax Incidence* knowledge point $$ \begin{aligned} &P_D = P_S + 3\ &60 - P_D = 2P_S \implies 60 - (P_S + 3) = 2P_S \implies 57 = 3P_S\ &P_S^* = 19,\quad P_D^* = 22,\quad q^* = 38\ &\text{The equilibrium quantity and prices are identical to part (b).} \end{aligned} $$ ## Calculate welfare changes Using the *Deadweight Loss* and *Welfare Analysis* knowledge points $$ \begin{aligned} &\Delta CS = -\frac{1}{2}(40 + 38)(22 - 20) = -78\ &\Delta PS = -\frac{1}{2}(40 + 38)(20 - 19) = -39\ &\text{Tax Revenue} = 3 \times 38 = 114\ &DWL = \frac{1}{2}(40 - 38)(3) = 3 \end{aligned} $$ ## Question 4 ### (a) * **Equilibrium Price ($P^*$):** $20$ * **Equilibrium Quantity ($Q^*$):** $40$ ### (b) * **Equilibrium Quantity ($q^*$):** $38$ * **Producer Price ($P_S^*$):** $19$ * **Consumer Price ($P_D^*$):** $22$ * **Tax Passed to Consumer:** $2$ per unit ### (c) * **Equilibrium Quantity ($q^*$):** $38$ * **Producer Price ($P_S$):** $19$ * **Consumer Price ($P_D$):** $22$ * **Comparison:** The economic incidence is identical to part (b); the statutory burden does not affect the final equilibrium outcome. ### (d) * **Change in Consumer Surplus ($\Delta CS$):** $-78$ * **Change in Producer Surplus ($\Delta PS$):** $-39$ * **Tax Revenue:** $114$ * **Deadweight Loss ($DWL$):** $3$ { "elements": [ { "type": "functiongraph", "params": [{"js": "60 - x", "latex": "P_D = 60 - Q"}, 0, 60], "properties": { "strokeColor": "#5583F2", "strokeWidth": 2, "name": "D", "withLabel": true } }, { "type": "functiongraph", "params": [{"js": "0.5 * x", "latex": "P_S = 0.5 * Q"}, 0, 60], "properties": { "strokeColor": "#F2557F", "strokeWidth": 2, "name": "S", "withLabel": true } }, { "type": "functiongraph", "params": [{"js": "0.5 * x + 3", "latex": "P_S + t"}, 0, 60], "properties": { "strokeColor": "#D92B54", "strokeWidth": 2, "name": "S + t", "withLabel": true } }, { "type": "point", "params": [[40, 20]], "properties": { "name": "E0 (40, 20)", "color": "#583C87", "size": 3, "withLabel": true } }, { "type": "point", "params": [[38, 22]], "properties": { "name": "E1 (38, 22)", "color": "#8C55F2", "size": 3, "withLabel": true } }, { "type": "point", "params": [[38, 19]], "properties": { "name": "Es (38, 19)", "color": "#8C55F2", "size": 3, "withLabel": true } }, { "type": "customzone", "params": [ { "points": [[38, 19], [38, 22], [40, 20]], "fillColor": "rgba(242, 85, 127, 0.3)", "fillOpacity": 0.3 } ], "properties": { "name": "DWL" } } ], "timestamps": [0.5, 1.0, 1.5] } { "subject": "Business", "question_type": "Multi-part", "knowledge_point": [ "Business", "Economics", "Tax Incidence" ] }

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QUESTION IMAGE

Question

Explanation:

Find the market equilibrium without taxes

Analyze tax on supplier

Analyze tax on demander

Calculate welfare changes

Answer:

Question 4

(a)

(b)

(c)

(d)